In [1]:
# Parameters
SWARM_PATH3 = "/home/kamran.karimi1/Project/git/Swarm/dataset/RidgeCrest/catalog_fmsearch.csv"
n_thresh = 0.001
SWARM_PATH4 = "/home/kamran.karimi1/Project/git/Swarm/dataset/RidgeCrest/momentTensors.pkl"
fetch the data: Shelly 2020¶
In [2]:
#--- extract the catalog (new)
import pandas as pd
#import matplotlib; matplotlib.use('agg')
import sys
from matplotlib import rc
import matplotlib
import matplotlib.pylab as plt
import numpy as np
from matplotlib import patches
import warnings
import matplotlib.ticker
import matplotlib as mpl
#from mpl_toolkits.mplot3d import Axes3D
import datetime
#import path
from math import *
import matplotlib.dates as mdates
from matplotlib import dates
import matplotlib.dates as md
import matplotlib.cm as cm
from matplotlib.font_manager import FontProperties
import itertools
import traceback
from scipy.ndimage import gaussian_filter
import math
def DrawFrame(ax, (alpha_xl,alpha_xr),(alpha_yb,alpha_yt),linewidth,LOG_X=None,LOG_Y=None):
[xlo,xhi,ylo,yhi] = ax.axis()
if LOG_X:
[xlo,xhi,junk,junk] = np.log10(ax.axis())
if LOG_Y:
[junk,junk,ylo,yhi] = np.log10(ax.axis())
lx = xhi - xlo
ly = yhi - ylo
xy = [xlo - alpha_xl * lx, ylo - alpha_yb * ly]
height = ly*(1+alpha_yb+alpha_yt)
width = lx*(1+alpha_xl+alpha_xr)
xy_end=[xy[0]+width,xy[1]+height]
if LOG_X:
xy[0] = 10 ** xy[0]
xy_end[0] = 10 ** xy_end[0]
if LOG_Y:
xy[1] = 10 ** xy[1]
xy_end[1] = 10 ** xy_end[1]
ax.add_patch( patches.Rectangle(xy=xy, width=xy_end[0]-xy[0],
height=xy_end[1]-xy[1], linewidth=linewidth,
clip_on=False,facecolor=None,edgecolor='black',fill=None) )
#--- add a new time attribute
def ConvertTime( df_in ):
df=df_in.copy()
df.insert(0,'date',pd.to_datetime(swarm[['year', 'month', 'day', 'hour', 'minute', 'second']]))
df.drop(['year', 'month', 'day', 'hour', 'minute', 'second'],axis=1,inplace=True)
return df
# #--- set path
# SWARM_PATH = './dataset/RidgeCrest/DataS1_noXYZ.txt' #--- comment if passed by argument
# DIR_OUTPT = '.'
# DIR_OUTPT_figs = '.'
# #--- store
# swarm = pd.read_csv( SWARM_PATH, sep = ',' ) #--- parse data
# swarm = ConvertTime( swarm ) #--- add new column 'date'
# #--- sort based on time
# swarm.sort_values(by=['date'],inplace=True)
# #--- reindex
# swarm.reset_index(inplace=True,drop=True)
# #--- rename cols
# swarm = swarm.rename(index=str,columns={'lat':'latitude','lon':'longitude','mag':'magnitude'})
# swarm.head()
In [3]:
mpl.rcParams.update(mpl.rcParamsDefault)
warnings.filterwarnings('ignore') #--- get rid of warnings
rc('text', usetex=True)
font = {'size' : 20}
matplotlib.rc('font', **font)
In [4]:
# #--- add a new time attribute
# def ConvertTime( df_in ):
# df=df_in.copy()
# df['date']=pd.to_datetime(df['Event ID'] +' ' + df['Origin Time'])
# df['Event ID']=df.index
# # df.insert(0,'date',pd.to_datetime(swarm[['year', 'month', 'day', 'hour', 'minute', 'second']]))
# df.drop(['Origin Time'],axis=1,inplace=True)
# return df
# #--- set path
# SWARM_PATH = './dataset/RidgeCrest/Dataset S2.txt' #--- comment if passed by command line
# DIR_OUTPT = '.' #'./dataset/RidgeCrest' #sys.argv[2]
# DIR_OUTPT_figs = '.' #'./dataset/figs' #'/Users/Home/Desktop/Tmp/txt' #'/Users/Home/Dropbox/Documents/papers/microSeismicityOklahoma/figs'
# #--- store
# swarm = pd.read_csv( SWARM_PATH, sep = ',' ) #--- parse data
# swarm = ConvertTime( swarm ) #--- add new column 'date'
# #--- sort based on time
# swarm.sort_values(by=['date'],inplace=True)
# #--- reindex
# swarm.reset_index(inplace=True,drop=True)
# #--- rename cols
# swarm = swarm.rename(index=str,columns={'Latitude':'latitude','Longitude':'longitude',
# 'Magnitude (SCEDC preferred)':'magnitude','Depth (km)':'depth'})
# swarm.head()
In [5]:
#--- remove nan
#swarm = swarm.dropna(subset=['magnitude'])
#swarm.info()
In [6]:
# #--- add a new time attribute
# def ConvertTime( df_in ):
# df=df_in.copy()
# df['date']=pd.to_datetime(df['Date']+' '+df['Time(UTC)'])
# # df['date']=pd.to_datetime(df['Event ID'] +' ' + df['Origin Time'])
# # df['Event ID']=df.index
# # df.insert(0,'date',pd.to_datetime(df_moment[['year', 'month', 'day', 'hour', 'minute', 'second']]))
# df.drop(['Time(UTC)','(Ml)','Mp','originalDepth','Solutions','VR','Date'],axis=1,inplace=True)
# return df
# #--- set path
# SWARM_PATH2 = './dataset/RidgeCrest/momentTensor.csv' #--- comment if passed by command line
# #--- store
# df_moment = pd.read_csv( SWARM_PATH2, sep = ',' ) #--- parse data
# df_moment = ConvertTime( df_moment ) #--- add new column 'date'
# #--- sort based on time
# df_moment.sort_values(by=['date'],inplace=True)
# #--- reindex
# df_moment.reset_index(inplace=True,drop=True)
# #--- rename cols
# df_moment = df_moment.rename(index=str,columns={'EventID':'Event ID','Lat.':'latitude',
# 'Long.':'longitude','Mw':'magnitude'})
# df_moment.head()
fetch tensors from the html files¶
- use event id's from the above catalog
In [7]:
# azimuth_t=[]
# azimuth_n=[]
# azimuth_p=[]
# plunge_t = []
# plunge_n = []
# plunge_p = []
# mt = []
# mn = []
# mp = []
# for items in df_moment.itertuples():
# if 1: #try:
# eventID = items[1]
# html_url='https://service.scedc.caltech.edu/MomentTensor/solutions/web_%s/ci%s_MT.html'%(eventID,eventID)
# # print html_url
# dff=pd.read_html(html_url)
# dff=dff[2] #--- eigenvalues and eigenmodes
# # if eventID not in list(swarm['Event ID']):
# # continue
# # #--- stress catalog
# # # if eventID == 38636511:
# # print eventID, df_st[df_st['Event ID']==eventID]['Origin Time'].iloc[0]-items[4]
# # print df_st[df_st['Event ID']==eventID]['Origin Time'].iloc[0],items[4]
# # #--- parse moment tensor
# azimuth_t.append(float(dff.iloc[2][3]))
# azimuth_n.append(float(dff.iloc[3][3]))
# azimuth_p.append(float(dff.iloc[4][3]))
# plunge_t.append(float(dff.iloc[2][2]))
# plunge_n.append(float(dff.iloc[3][2]))
# plunge_p.append(float(dff.iloc[4][2]))
# mt.append(float(dff.iloc[2][1]))
# mn.append(float(dff.iloc[3][1]))
# mp.append(float(dff.iloc[4][1]))
# assert float(dff.iloc[2][1]) > 0.0
# assert float(dff.iloc[4][1]) < 0.0
insert as columns¶
In [8]:
# df_moment.insert(len(df_moment.keys()),'mt',mt)
# df_moment.insert(len(df_moment.keys()),'Azimuth(T)',azimuth_t)
# df_moment.insert(len(df_moment.keys()),'Plunge(T)',plunge_t)
# df_moment.insert(len(df_moment.keys()),'mn',mn)
# df_moment.insert(len(df_moment.keys()),'Azimuth(N)',azimuth_n)
# df_moment.insert(len(df_moment.keys()),'Plunge(N)',plunge_n)
# df_moment.insert(len(df_moment.keys()),'mp',mp)
# df_moment.insert(len(df_moment.keys()),'Azimuth(P)',azimuth_p)
# df_moment.insert(len(df_moment.keys()),'Plunge(P)',plunge_p)
common events between the two catalogs¶
In [9]:
# df_moment.index=df_moment['Event ID']
# common_elm = list(set(df_moment['Event ID']) & set(swarm['Event ID']))
# df_moment = df_moment.loc[common_elm]
# df_moment.reset_index(drop=True, inplace=True)
# df_moment.head()
moment tensors scedc¶
Column legend:¶
EVID : Event Id
ET : Earthquake Type
MAG : Event Magnitude
M : Magnitude Type
LAT : Latitude
LON : Longitude
DEPTH : Earthquake Depth
Q : Quality
NPH : Number of phases or arrivals
WRMS : Weighted RMS
ERHOR : Horizontal Error (location uncertainty that accompanies the location)
ERDEP : Depth Error (standard deviation of depth estimate)
ERTIME : Origin Time Error (standard deviation of origin time)
STRIKE : Strike of fault plane
DIP : Dip of fault plane
RAKE : Rake of fault plane
FPUC : Fault Plane Uncertainty in degrees
APUC : Auxialiary Plane Uncertainty in degrees
NPPL : Number of P Polarities
MFRAC : Fraction Misfit Polarities
FMQ : Focal Mechanism Quality
PROB : Probability true mechanism is "close" to preferred solution
STDR : Station Distribution
NSPR : Number of S/P Ratios
MAVG : Average log10(S/P) Misfit
In [10]:
#--- add a new time attribute
def ConvertTime( df_in ):
df=df_in.copy()
# display(df.head())
df.insert(loc=2, column='date', value=pd.to_datetime(df['#YYY/MM/DD']+' '+df['HH:mm:SS.ss']))
# df['date']=pd.to_datetime(df['Event ID'] +' ' + df['Origin Time'])
# df['Event ID']=df.index
# df.insert(0,'date',pd.to_datetime(df_moment[['year', 'month', 'day', 'hour', 'minute', 'second']]))
df.drop(['#YYY/MM/DD','HH:mm:SS.ss', u'ET', u'GT',u'M', u'Q', u'NPH', u'WRMS', u'ERHOR', u'ERDEP',
u'ERTIME', u'STRIKE', u'DIP', u'RAKE', u'FPUC', u'APUC', u'NPPL',
u'MFRAC', u'FMQ', u'PROB', u'STDR', u'NSPR', u'MAVG'],axis=1,inplace=True)
return df
#--- set path
#SWARM_PATH3 = './dataset/RidgeCrest/catalog_fmsearch.csv' #--- comment if passed by command line
DIR_OUTPT = '.'
DIR_OUTPT_figs = '.'
#--- store
df_moment = pd.read_csv( SWARM_PATH3, sep = ',' ) #--- parse data
df_moment = ConvertTime( df_moment ) #--- add new column 'date'
#--- sort based on time
df_moment.sort_values(by=['date'],inplace=True)
#--- reindex
df_moment.reset_index(inplace=True,drop=True)
#--- rename cols
df_moment = df_moment.rename(index=str,columns={'EVID':'Event ID','LAT':'latitude',
'LON':'longitude','MAG':'magnitude', 'DEPTH':'depth'})
#df_moment = df_moment.iloc[:32]
df_moment.head()
#df_moment.keys()
Out[10]:
In [11]:
df_moment.info()
fetch angles¶
In [12]:
# def func(x):
# try:
# html_url = x
# dff=pd.read_html(html_url)
# dff=dff[3] #--- eigenvalues and eigenmodes
# #--- parse moment tensor
# assert dff.iloc[0]['Axis'] == 'P'
# assert dff.iloc[1]['Axis'] == 'T'
# assert dff.iloc[1]['Azimuth'][-4:-1] == '&de'
# assert dff.iloc[0]['Azimuth'][-4:-1] == '&de'
# assert dff.iloc[1]['Plunge'][-4:-1] == '&de'
# assert dff.iloc[0]['Plunge'][-4:-1] == '&de'
# azimuth_t = float(dff.iloc[1]['Azimuth'][:-4])
# azimuth_p = float(dff.iloc[0]['Azimuth'][:-4])
# plunge_t = float(dff.iloc[1]['Plunge'][:-4])
# plunge_p = float(dff.iloc[0]['Plunge'][:-4])
# return (azimuth_t,plunge_t,azimuth_p,plunge_p)
# except:
# return (None, None, None, None )
# df_moment['html']=df_moment['Event ID'].apply(lambda x: 'https://service.scedc.caltech.edu/FocMech/ci%s.cifm1.html'%(x))
# s_series = df_moment['html'].apply(func)
# df_moment['Azimuth(T)'] = s_series.apply(lambda x: x[0])
# df_moment['Plunge(T)'] = s_series.apply(lambda x: x[1])
# df_moment['Azimuth(P)'] = s_series.apply(lambda x: x[2])
# df_moment['Plunge(P)'] = s_series.apply(lambda x: x[3])
# df_moment.drop(['html'],axis=1,inplace=True)
In [13]:
df_moment.head()
Out[13]:
save data frame¶
In [14]:
#SWARM_PATH4 = './dataset/RidgeCrest/momentTensors.pkl' #--- comment if passed by argument
#df_moment.to_pickle('./dataset/RidgeCrest/momentTensors.pkl')
swarm=pd.read_pickle(SWARM_PATH4)
In [15]:
#--- plot spatial map
#--- fault map california: temporal evolution of events
def DataFrameSubSet( df, column, (xmin,xmax) ):
return df[ ( df[column] >= xmin ) &
( df[column] < xmax ) ]
#--- subset of data
swarm_lohi = swarm.copy()#DataFrameSubSet( swarm,
# 'date',
# ( pd.to_datetime('2010-04-04'), pd.to_datetime('2010-06-26') ) )
swarm_lohi.plot.scatter('longitude','latitude',
s=3**(swarm_lohi['magnitude']),
c='date',cmap='jet',
alpha=0.1,figsize=(5,4)) #--- plot
# swarm_lohi.plot.scatter('longitude','depth',
# s=3**(swarm_lohi['magnitude']),
# c='date',cmap='jet',
# alpha=0.1,figsize=(5,4)) #--- plot
# swarm_lohi.plot.scatter('latitude','depth',
# s=3**(swarm_lohi['magnitude']),
# c='date',cmap='jet',
# alpha=0.1,figsize=(5,4)) #--- plot
plt.show()
#plt.savefig('%s/map.png'%DIR_OUTPT_figs,dpi=150,bbox_inches='tight')
#plt.figure(figsize=(6,6)).gca(projection='3d')
#plt.xlabel('Long')
#plt.ylabel('Lat')
#plt.scatter(swarm_lohi['longitude'],
# swarm_lohi['latitude'],
# swarm_lohi['depth']) #s=10*swarm['magnitude'],cmap='jet') #--- plot
make movies¶
In [16]:
# import os
# class makeDATA:
# def __init__(self, write, read = None ):
# self.wirite = write
# self.read = read # embedded object: attrs (coord, lohi, type, vel)
# def __del__( self ):
# self.wirite.close()
# def Map(self, coord, comnt, *args ):
# nAtom = len(coord)
# self.wirite.write('%s\n%s\n'%(nAtom,comnt))
# for i in coord:
# ndime = len( coord[i] )
# self.wirite.write('%s\t'% i)
# # self.wirite.write('%d\t'% type[i])
# for idime in xrange( ndime ):
# self.wirite.write('%e\t'%coord[i][idime] )
# if args:
# for dics in args:
# # if type( dics[ i ] == type( 1 ) ):
# # self.wirite.write( '%d\t' % dics[ i ] )
# # else:
# VAL = 0.0 if abs(dics[ i ])<1.0e-15 else dics[ i ]
# self.wirite.write( '%s\t' % VAL )
# self.wirite.write( '\n' )
# else:
# self.wirite.write( '\n' )
# self.wirite.flush()
# self.wirite.close()
# swarm_lohi.sort_values(by='date',inplace=True)
# coord_length=swarm_lohi['longitude'].apply(lambda x:[x])+swarm_lohi['latitude'].apply(lambda x:[x])
# Magnitude = np.exp(swarm_lohi['magnitude'])/20000
# makeDATA( open( '%s/map.xyz'%DIR_OUTPT, 'w' ), None ).Map( coord_length.to_dict(), 'ITIME=%s'%0, Magnitude.to_dict()) #--- instantanuous
# EVENT_ID = Magnitude.keys()
# EVENT_ID = map(int,EVENT_ID)
# EVENT_ID.sort()
# cords={}
# mag={}
# t0 = None
# os.system('rm %s/temporalMap.xyz'%DIR_OUTPT)
# for j_event,indexx in zip(EVENT_ID,xrange(10000)):
# # print j_event
# t = swarm_lohi['date'].iloc[ j_event ]
# if not t0:
# t0 = t
# assert t >= t0, 't0=%s,t=%s'%( t0, t )
# #--- temporal map
# cords[ j_event ] = coord_length[ j_event ]
# mag[ j_event ] = Magnitude[ j_event ]
# itime=swarm_lohi[ 'date' ].iloc[ j_event ]
# tstr='%s-%s'%(itime.strftime("%x"), itime.strftime("%X"))
# makeDATA( open( '%s/temporalMap.xyz'%DIR_OUTPT, 'a' ), None ).Map( cords, 'ITIME=%s'%itime, mag ) #--- instantanuous
# t0 = t
In [17]:
# #--- plot timeseries
class Tlohi:
def __init__(self,lo,hi):
self.lo = lo
self.hi = hi
# fig=plt.figure(figsize=(8,4))
# ax=fig.add_subplot(111)
# plt.xlabel('Time')
# plt.ylabel('M')
# plt.ylim(swarm['magnitude'].min(),swarm['magnitude'].max())
# tt=swarm[swarm['magnitude']==swarm['magnitude'].sort_values(ascending=False).iloc[3]]['date']
# plt.xlim(tt-datetime.timedelta(days=30),tt+datetime.timedelta(days=30))# pd.to_datetime('2014-12-04'),pd.to_datetime('2015-06-1'))
# #plt.xlim(swarm['date'].min(),pd.to_datetime('2010-07-20'))
# plt.scatter(swarm['date'],swarm['magnitude'],
# s=2*np.exp(swarm['magnitude']),
# alpha=0.2)
# #myTlohi = Tlohi( pd.to_datetime('2010-04-08'),
# # pd.to_datetime('2010-07-01'))
# #plt.plot([myTlohi.lo,myTlohi.lo],
# # [-2,7],'r-')
# #plt.plot([myTlohi.hi,myTlohi.hi],
# # [-2,7],'r-')
# fig.autofmt_xdate()
# plt.savefig('%s/timeSeries.png'%DIR_OUTPT_figs,dpi=150,bbox_inches='tight')
# plt.show()
In [18]:
#--- freq-magnitude relation
import sys
def histogramACCUMLTD( slist ):
assert type( slist ) == type( [] ), 'arg must be a list. a %s is given!' %( type( slist ) )
d = {}
for item in slist:
try:
d[ item ] += 1
except:
d[ item ] = 1
keys = d.keys()
keys.sort()
cdf = 0.0
xi = min( slist ) - 1.0e-6
xf = max( slist ) + 1.0e-6
npoin = len( slist )
adict = {}
for ikey, index in zip( keys, xrange( sys.maxint ) ):
adict[ index ] = [ xi, ikey, cdf ]
cdf += 1.0 * d[ ikey ] # / npoin
xi = ikey
adict[ index + 1 ] = [ xi, xf, cdf ]
return adict
#--- set min/max time to avoid temporal incompletenesss issue
swarm_copy = swarm.copy()#DataFrameSubSet( swarm,
# 'date',
# ( myTlohi.lo,
# myTlohi.hi ) )
#--- accumulated histogram
N = len(swarm_copy['magnitude'])
slist=np.array(swarm_copy['magnitude'])
slist.sort()
d = histogramACCUMLTD( slist.tolist() )
keys=d.keys()
keys.sort()
#--- plot
fig= plt.figure(figsize=(3,3))#,dpi=150)
ax = fig.add_subplot(111)
ax.axis([-1,6,.9,1e5])
ax.set_yscale('log')
#--- add major xticks
xmin=np.ceil(ax.axis()[0])
xmax=np.floor(ax.axis()[1])
nbin = xmax - xmin
ax.set_xticks(np.linspace(ax.axis()[0],ax.axis()[1],int(nbin)+1))
#--- add major yticks
ymin=np.ceil(np.log10(ax.axis()[2]))
ymax=np.floor(np.log10(ax.axis()[3]))
nbin = ymax - ymin
ax.set_yticks(np.logspace(ymin,ymax,int(nbin)+1))
#--- put minor bins
#locmin = matplotlib.ticker.LogLocator(base=10.0,subs=(0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1),numticks=12)
#ax.xaxis.set_minor_locator(locmin)
#ax.xaxis.set_minor_formatter(matplotlib.ticker.NullFormatter())
#--- put minor bins y
locmin = matplotlib.ticker.LogLocator(base=10.0,subs=(0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1),numticks=12)
ax.yaxis.set_minor_locator(locmin)
ax.yaxis.set_minor_formatter(matplotlib.ticker.NullFormatter())
ax.tick_params(axis='y',left=True, right=True,which='both')
ax.tick_params(axis='x',bottom=True, top=True,which='both')
xmin=swarm_copy['magnitude'].min()
xmax=swarm_copy['magnitude'].max()
dx=0.1
junk = ax.hist( swarm_copy['magnitude'],
bins=int((xmax-xmin)/dx),
label='histogram',color='silver') #--- histogram
xx=[];yy=[]
for ikey in keys:
xx.append(d[ikey][0])
yy.append(N-d[ikey][2])
ax.plot(xx,yy,
linestyle='-', drawstyle='steps-post',color='black',
linewidth=1.0) #--- accumulated
b=0.8
ax.plot([2.5,6],[1e4, 1e4* 10**(-b*(6-2.5))],'r-.',linewidth=1)
DrawFrame(ax, (0.2,0.06),(0.32,0.1),0.01,LOG_Y=True)
#plt.savefig('%s/gr.png'%DIR_OUTPT_figs,dpi=150,bbox_inches='tight')#,transparent=True)
plt.show()
In [19]:
#--- estimate b by varying the mc value
from math import *
import scipy.stats
#--- set min/max time to avoid temporal incompletenesss issue
swarm_copy = swarm.copy()#DataFrameSubSet( swarm.copy()#,
# 'date', #
# ( myTlohi.#lo,
# myTlohi.hi# ) )
#--- plot distributions (Nm)
fig = plt.figure(figsize=(12,4))
ax=fig.add_subplot(131)
ax.set_xlabel('$m$')
ax.set_ylabel('$N(mag.>m)$')
xmin = np.floor(swarm_copy['magnitude'].min())
xmax = np.ceil(swarm_copy['magnitude'].max())
ax.set_xticks(np.linspace(xmin,xmax,int(xmax-xmin)/1+1))
ax.set_xlim(xmin,xmax)
#plt.ylim(1,1e5)
ax.set_yscale('log')
for ikey in keys:
ax.plot([d[ikey][0],d[ikey][1]],
[N-d[ikey][2],N-d[ikey][2]],
'-',color='black') #--- accumulated
junk = ax.hist( swarm_copy['magnitude'],
bins=64,
label='histogram') #--- histogram
#--- list of magnitudes
mm_list = swarm_copy['magnitude'].to_list()
mm_list = np.sort(mm_list)
#--- b vs mc
ax2=fig.add_subplot(132)
ax2.set_xticks(np.linspace(-1.0,3.0,5))
#ax2.set_ylim(0,1.8)
#ax4 = ax2.twinx()
#ax4.set_yscale('log')
#ax4.set_ylim(1e-16,)
#plt.xlim(0.0,1.5)
ax2.set_xlabel('$m_c$')
ax2.set_ylabel('$b$')
#ax4.set_ylabel(r'$p_{val}$',labelpad=-70)
#--- bvalue bhatacharya eq. 5
DM = 0.1
n = 30
#---
MC = []
B = []
Err_B = []
pval = []
for mc_new in [0.05+i*0.1 for i in xrange(n)]: #--- m values are quantized (+- 0.1)!
mlist = swarm_copy[ swarm_copy['magnitude']-mc_new>=0.0]['magnitude']
m_mean=mlist.mean()
assert m_mean-mc_new > 0.0, 'm_mean=%s,mc=%s'%( m_mean, mc )
k_mean = (m_mean-mc_new)/DM
b_value = log(np.exp(1),10)*log(1+DM/(m_mean-mc_new))/DM
nsamp = len(mlist)
# err_b = 1.96*(b_value/nsamp/log(10,exp(1.0)))**0.5
err_b = 2*(k_mean*(k_mean+1)/nsamp)**0.5/log(10,exp(1.0)) #--- Guttorp and Hopkins (1986) eq.(4)
# #--- bvalue bhatacharya eq. 6
# #--- accumulated histogram
# slist = mm_list[ mm_list>=mc_new ]
# slist.sort()
# NN = len(slist)
# cdf = histogramACCUMLTD( slist.tolist() )
# #--- bvalue bhatacharya eq. 6
# n_cdf=len(cdf)-1
# bi = []
# for i in xrange(n_cdf):
# mi = cdf[ i ][ 0 ]
# Ni = NN - cdf[ i ][ 2 ]
# bij = []
# for j in xrange(n_cdf):
# mj = cdf[ j ][ 0 ]
# Nj = NN - cdf[ j ][ 2 ]
# if i == j: continue
# slope = ( log( Nj, 10 ) - log( Ni, 10 ) ) / ( mj - mi )
# assert not np.isnan(slope)
# bij.append( slope )
# bi.append( np.median( bij ) )
# bval_2nd = -np.median( bi )
# err_b2nd = np.std(bi)/(len(bi))**0.5
#--- plot b vs mc
ax2.errorbar([mc_new],[b_value],yerr=err_b,marker='o',color='black')
# ax2.errorbar([mc_new],[bval_2nd],yerr=err_b2nd, marker='o',color='red')
#---
MC.append(mc_new)
B.append(b_value)
Err_B.append(err_b)
#--- p-value (by hand)
# (dmax,pval2nd) = scipy.stats.kstest( mlist, lambda x: 1.0-10**(-b_value*(x-mc_new)))
# ax4.plot([mc_new],[pval2nd],marker='o',color='red')
# pval.append(pval2nd)
#--- choose the range of mc
mc_range=[1.5,1.5]
index_tf = [i and j for i, j in zip(mc_range[0]<=np.array(MC),np.array(MC)<mc_range[1])]
bvall = np.array(B)[index_tf]
Err_B = np.array(Err_B)[index_tf]
#--- b vs mc: vertical lines
#ax2.plot([mc_range[0],mc_range[0]],[np.min(B),np.max(B)],'--r')
#ax2.plot([mc_range[1],mc_range[1]],[np.min(B),np.max(B)],'--r')
#--- N vs m: vertical line
#ax.plot([mc_range[0]+DM/2,mc_range[0]+DM/2],
# [1,len(swarm_copy['magnitude'])],'--r')
#--- n*10*bm (rescaled)
bval=0.8 #np.mean(bvall)
#bval2=0.8
ax3=fig.add_subplot(133)
ax3.set_xlabel('$m$')
#ax3.set_ylabel(r'$N\times10^{%s\times m}$'%bval)
ax3.set_ylabel(r'$N\times10^{%s\times m}$'%bval)
ax3.yaxis.set_label_position("right")
ax3.yaxis.tick_right()
ax3.set_yscale('log')
ax3.set_xticks(np.linspace(xmin,xmax,int(xmax-xmin)/1+1))
ax3.set_xlim(xmin,xmax)
#ax3.set_ylim(1e3,1e6)
#ax3.set_xticks(np.linspace(ax3.axis()[0],ax3.axis()[1],4))
for ikey in keys: #--- rescaled
c = 10**(bval*d[ikey][0])
ax3.plot([d[ikey][0],d[ikey][1]],
[c*(N-d[ikey][2]),c*(N-d[ikey][2])],'-',color='black',
) #--- accumulated
# c = 10**(bval2*d[ikey][0])
# ax3.plot([d[ikey][0],d[ikey][1]],
# [c*(N-d[ikey][2]),c*(N-d[ikey][2])],'-',color='red',
# ) #--- accumulated
ax3.plot([mc_range[0]+DM/2,mc_range[0]+DM/2], #--- vertical line
[len(swarm_copy[swarm_copy['magnitude']>mc_range[0]])*10**(bval*mc_range[0])/10,
len(swarm_copy[swarm_copy['magnitude']>mc_range[0]])*10**(bval*mc_range[0])],'--r')
#plt.plot(MC, pval,'-o',color='black')
fig.tight_layout(w_pad=-0.5)
#fig.savefig('%s/b.png'%DIR_OUTPT_figs,dpi=75)
plt.show()
In [20]:
#--- estimate b by varying the mc value
from math import *
import scipy.stats
#--- set min/max time to avoid temporal incompletenesss issue
swarm_copy = swarm.copy()#DataFrameSubSet( swarm.copy()#,
# 'date', #
# ( myTlohi.#lo,
# myTlohi.hi# ) )
#--- plot distributions (Nm)
fig = plt.figure(figsize=(12,4))
ax=fig.add_subplot(131)
ax.set_xlabel('$m$')
ax.set_ylabel('$N(mag.>m)$')
xmin = np.floor(swarm_copy['magnitude'].min())
xmax = np.ceil(swarm_copy['magnitude'].max())
ax.set_xticks(np.linspace(xmin,xmax,int(xmax-xmin)/1+1))
ax.set_xlim(xmin,xmax)
#plt.ylim(1,1e5)
ax.set_yscale('log')
for ikey in keys:
ax.plot([d[ikey][0],d[ikey][1]],
[N-d[ikey][2],N-d[ikey][2]],
'-',color='black') #--- accumulated
junk = ax.hist( swarm_copy['magnitude'],
bins=64,
label='histogram') #--- histogram
#--- list of magnitudes
mm_list = swarm_copy['magnitude'].to_list()
mm_list = np.sort(mm_list)
#--- b vs mc
ax2=fig.add_subplot(132)
ax2.set_xticks(np.linspace(0,1,5,endpoint=True))
#ax2.set_ylim(0.5,1.0)
ax4 = ax2.twinx()
ax4.set_yscale('log')
ax4.set_ylim(1e-16,)
ax2.set_xlabel('$m_c$')
ax2.set_ylabel('$b$')
ax4.set_ylabel(r'$p_{val}$',labelpad=-10)
ax4.set_xticks(np.linspace(0,1,5,endpoint=True))
#--- bvalue bhatacharya eq. 5
DM = 0.01
n = 200
#---
MC = []
B = []
Err_B = []
pval = []
for mc_new in [i*DM for i in xrange(n)]: #--- m values are quantized (+- 0.1)!
mlist = swarm_copy[ swarm_copy['magnitude']-mc_new>=0.0]['magnitude']
m_mean=mlist.mean()
assert m_mean-mc_new > 0.0#, 'm_mean=%s,mc=%s'%( m_mean, mc )
k_mean = (m_mean-mc_new)/DM
b_value = log(np.exp(1),10)*log(1+DM/(m_mean-mc_new))/DM
nsamp = len(mlist)
err_b = 1.96 * b_value / nsamp ** 0.5 #1.96*(b_value/nsamp/log(10,exp(1.0)))**0.5
# err_b = 2*(k_mean*(k_mean+1)/nsamp)**0.5/log(10,exp(1.0)) #--- Guttorp and Hopkins (1986) eq.(4)
# #--- bvalue bhatacharya eq. 6
# #--- accumulated histogram
# slist = mm_list[ mm_list>=mc_new ]
# slist.sort()
# NN = len(slist)
# cdf = histogramACCUMLTD( slist.tolist() )
# #--- bvalue bhatacharya eq. 6
# n_cdf=len(cdf)-1
# bi = []
# for i in xrange(n_cdf):
# mi = cdf[ i ][ 0 ]
# Ni = NN - cdf[ i ][ 2 ]
# bij = []
# for j in xrange(n_cdf):
# mj = cdf[ j ][ 0 ]
# Nj = NN - cdf[ j ][ 2 ]
# if i == j: continue
# slope = ( log( Nj, 10 ) - log( Ni, 10 ) ) / ( mj - mi )
# assert not np.isnan(slope)
# bij.append( slope )
# bi.append( np.median( bij ) )
# bval_2nd = -np.median( bi )
# err_b2nd = np.std(bi)/(len(bi))**0.5
#--- plot b vs mc
ax2.errorbar([mc_new],[b_value],yerr=err_b,marker='o',color='black')
# ax2.errorbar([mc_new],[bval_2nd],yerr=err_b2nd, marker='s',color='green')
#---
MC.append(mc_new)
B.append(b_value)
Err_B.append(err_b)
#--- p-value (by hand)
(dmax,pval2nd) = scipy.stats.kstest( mlist, lambda x: 1.0-10**(-b_value*(x-mc_new)))
ax4.plot([mc_new],[pval2nd],marker='o',color='red')
pval.append(pval2nd)
# print b_value, pval2nd
xmin = min(MC)
xmax = max(MC)
ax2.set_xticks(np.linspace(xmin,xmax,int(xmax-xmin)/.2))
ax2.set_xlim(xmin,xmax)
#--- choose the range of mc
mc_range=[1.5,1.5]
index_tf = [i and j for i, j in zip(mc_range[0]<=np.array(MC),np.array(MC)<mc_range[1])]
bvall = np.array(B)[index_tf]
Err_B = np.array(Err_B)[index_tf]
#--- b vs mc: vertical lines
#ax2.plot([mc_range[0],mc_range[0]],[np.min(B),np.max(B)],'--r')
#ax2.plot([mc_range[1],mc_range[1]],[np.min(B),np.max(B)],'--r')
#--- N vs m: vertical line
#ax.plot([mc_range[0]+DM/2,mc_range[0]+DM/2],
# [1,len(swarm_copy['magnitude'])],'--r')
#--- n*10*bm (rescaled)
bval=0.8 #np.mean(bvall)
ax2.plot([xmin,xmax],[bval,bval],'--r')
#bval2=0.8
ax3=fig.add_subplot(133)
ax3.set_xlabel('$m$')
#ax3.set_ylabel(r'$N\times10^{%s\times m}$'%bval)
ax3.set_ylabel(r'$N\times10^{%s\times m}$'%bval)
ax3.yaxis.set_label_position("right")
ax3.yaxis.tick_right()
ax3.set_yscale('log')
xmin = np.floor(swarm_copy['magnitude'].min())
xmax = np.ceil(swarm_copy['magnitude'].max())
ax3.set_xticks(np.linspace(xmin,xmax,int(xmax-xmin)/1+1))
ax3.set_xlim(xmin,xmax)
#ax3.set_ylim(1e3,1e6)
#ax3.set_xticks(np.linspace(ax3.axis()[0],ax3.axis()[1],4))
for ikey in keys: #--- rescaled
c = 10**(bval*d[ikey][0])
ax3.plot([d[ikey][0],d[ikey][1]],
[c*(N-d[ikey][2]),c*(N-d[ikey][2])],'-',color='black',
) #--- accumulated
# c = 10**(bval2*d[ikey][0])
# ax3.plot([d[ikey][0],d[ikey][1]],
# [c*(N-d[ikey][2]),c*(N-d[ikey][2])],'-',color='red',
# ) #--- accumulated
ax3.plot([mc_range[0]+DM/2,mc_range[0]+DM/2], #--- vertical line
[len(swarm_copy[swarm_copy['magnitude']>mc_range[0]])*10**(bval*mc_range[0])/10,
len(swarm_copy[swarm_copy['magnitude']>mc_range[0]])*10**(bval*mc_range[0])],'--r')
#plt.plot(MC, pval,'-o',color='black')
# mc_new = 0.5
# b_value = 0.94
# ax2.scatter([mc_new],[b_value],marker='s',color='green')
# mlist = swarm_copy[ swarm_copy['magnitude']-mc_new>=0.0]['magnitude']
# (dmax,pval2nd) = scipy.stats.kstest( mlist, lambda x: 1.0-10**(-b_value*(x-mc_new)))
# ax4.plot([mc_new],[pval2nd],marker='o',color='green')
fig.tight_layout(w_pad=-0.5)
#fig.savefig('%s/b.png'%DIR_OUTPT_figs,dpi=75)
plt.show()
In [21]:
##--- estimate b and mc
#
#
#with path.Path('/Users/Home/Desktop/Tmp/txt/myPYlibs'):
# import plfit
# import plvar
# import plpva
#
##--- set min/max time to avoid temporal incompletenesss issue
#swarm_copy = swarm.copy()#DataFrameSubSet( swarm,
# # 'date',
# # ( myTlohi.lo,
# # myTlohi.hi ) )
#
##--- power law fit clauset
#n_samp = 1000
#n_chunk = len( swarm_copy ) / n_samp
#
#i = 0
#fig = plt.figure(figsize=(8,4))
#ax = fig.add_subplot(111)
#ax.set_ylabel('m')
#ax2=ax.twinx()
#ax.scatter(swarm_copy['date'],swarm_copy['magnitude'],
# alpha=0.1)
#
#fig2 = plt.figure(figsize=(8,4))
#ax21 = fig2.add_subplot(111)
#ax21.set_ylabel('m')
#ax21.scatter(swarm_copy['date'],swarm_copy['magnitude'],
# alpha=0.1)
#
#MC = []
#B = []
#for j in xrange(n_chunk):
# Mlist = 10**(swarm_copy.iloc[i:i+n_samp]['magnitude'])
# fit = plfit.plfit( np.array(Mlist) ) #--- clauset
# mc = log(fit[1],10) #--- completeness mag.
# bval = fit[0]-1
# MC.append(mc)
# B.append(bval)
## print mc, bval
# ax2.plot([swarm_copy.iloc[i:i+n_samp]['date'].min(),swarm_copy.iloc[i:i+n_samp]['date'].max()],
# [bval,bval],'-',color='red')
#
# ax21.plot([swarm_copy.iloc[i:i+n_samp]['date'].min(),swarm_copy.iloc[i:i+n_samp]['date'].max()],
# [mc,mc],'-',color='red')
#
# i += n_samp
#Mlist = 10**(swarm_copy.iloc[i:i+len(swarm_copy)%n_samp]['magnitude'])
#fit = plfit.plfit( np.array(Mlist) ) #--- clauset
#mc = log(fit[1],10) #--- completeness mag.
#bval = fit[0]-1
#MC.append(mc)
#B.append(bval)
#
##---- plot bval
#ax2.plot([swarm_copy.iloc[i:i+n_samp]['date'].min(),swarm_copy.iloc[i:i+n_samp]['date'].max()],
# [bval,bval],'-',color='red')
#ax2.tick_params(colors='red')
#ax2.set_ylabel('b',color='red')
#ax.set_xlabel('Date')
##print mc, bval
#fig.savefig('%s/b.png'%DIR_OUTPT_figs,dpi=75)
##--- plot mc
#ax21.plot([swarm_copy.iloc[i:i+n_samp]['date'].min(),swarm_copy.iloc[i:i+n_samp]['date'].max()],
# [mc,mc],'-',color='red',label='mc')
#plt.legend()
#ax21.set_xlabel('Date')
#
##n, bins, patches = plt.hist(B, 50)
#
##--- error estimate
##[ error_b, error_mc, ntail ] = [ 0.0, 0.0, 0.0 ]
##[error_b, error_mc, ntail] = plvar.plvar(np.array(Mlist), 'silent')
##error_mc = log(1.0+error_mc/fit[1],10) #--- log(1+dM/M)
#plt.savefig('%s/mc.png'%DIR_OUTPT_figs,dpi=75)
In [22]:
# #--- goodness of the fit
# n_samp = 1000
# n_chunk = len( swarm_copy ) / n_samp
# ncols=4
# nrows = n_chunk / ncols + int(np.ceil(1.0*( len(swarm_copy) % n_samp) / n_samp))
# i = 0
# plt.figure(figsize=(ncols*4,nrows*4))
# for j in xrange(n_chunk):
# Mlist = 10**(swarm_copy.iloc[i:i+n_samp]['magnitude'])
# fit = plfit.plfit( np.array(Mlist) ) #--- clauset
# mc = log(fit[1],10) #--- completeness mag.
# bval = fit[0]-1
# # [error_b, error_mc, ntail] = plvar.plvar(Mlist, 'silent') #--- error
# plt.subplot(nrows,ncols,j+1)
# Mlist=np.log10(Mlist)
# nc = len(Mlist[Mlist>=mc])
# error_b = (bval / nc / log(10.0) )**0.5
# hist,bins = np.histogram(Mlist,bins=1024)
# plt.plot(bins[:-1],-hist.cumsum()+len(Mlist))#,marker='o',markersize=6,linestyle='None')
# xc=0.5*(bins[:-1]+bins[1:])
# plt.plot(xc, len(Mlist[Mlist>=mc])*10**(-bval*(xc-mc)),'r',label='$b=%2.1f\pm%3.2f$'%(bval,error_b))
# plt.plot([mc,mc],[1,len(Mlist[Mlist>=mc])],label='$mc=%2.1f$'%(mc)) # len(Mlist[Mlist>=mc])*10**(-bval*(xc-mc)),'r')
# plt.yscale('log')
# plt.xlim(swarm_copy['magnitude'].min(),swarm_copy['magnitude'].max())
# plt.ylim(1,n_samp*10)
# if j == 0:
# plt.ylabel('N(size>m)')
# plt.xlabel('m')
# plt.legend()
# i += n_samp
# Mlist = 10**(swarm_copy.iloc[i:i+len(swarm_copy)%n_samp]['magnitude'])
# fit = plfit.plfit( np.array(Mlist) ) #--- clauset
# mc = log(fit[1],10) #--- completeness mag.
# bval = fit[0]-1
# Mlist=np.log10(Mlist)
# nc = len(Mlist[Mlist>=mc])
# error_b = (bval / nc / log(10.0) )**0.5
# hist,bins = np.histogram(Mlist,bins=1024)
# plt.subplot(nrows,ncols,j+2)
# plt.plot(bins[:-1],-hist.cumsum()+len(Mlist))#,marker='o',markersize=6,linestyle='None')
# xc=0.5*(bins[:-1]+bins[1:])
# plt.plot(xc, len(Mlist[Mlist>=mc])*10**(-bval*(xc-mc)),'r',label='$b=%2.1f\pm%3.2f$'%(bval,error_b))
# plt.plot([mc,mc],[1,len(Mlist[Mlist>=mc])],label='$m_c=%2.1f$'%(mc)) # len(Mlist[Mlist>=mc])*10**(-bval*(xc-mc)),'r')
# plt.yscale('log')
# plt.xlim(swarm_copy['magnitude'].min(),swarm_copy['magnitude'].max())
# plt.ylim(1,n_samp)
# plt.legend()
# plt.savefig('%s/b_mult.png'%DIR_OUTPT_figs,dpi=75,bbox_inches='tight')
In [23]:
# #--- plot complete catalog
# def ConvertDailyRate(hist, bin_edges ):
# #---convert data to daily rate
# t0 = pd.to_datetime( bin_edges[ 0 ] )
# t1 = pd.to_datetime( bin_edges[ 1 ] )
# delta_t = ( t1 - t0 ).total_seconds() / ( 60 * 60*24)
# hist *= ( bin_edges[ 1 ] - bin_edges[ 0 ] ) / delta_t
# def ActivityRate( swarm ):
# nbins = int( (swarm['date'].max()-swarm['date'].min()).days*4 ) #--- number of bins
# tmax = swarm['date'].max().value #--- min/max
# tmin = swarm['date'].min().value
# hist, bin_edges = np.histogram(swarm['date'].apply(lambda x:x.value),
# bins=np.linspace(tmin,tmax,nbins+1,endpoint=True),density=True) #--- probability dist.
# hist *= len( swarm['date'] ) #--- int(hist).dt=n
# cumm_number = np.cumsum(hist)*(bin_edges[1]-bin_edges[0]) #--- accumulated number
# ConvertDailyRate( hist, bin_edges ) #--- daily activity
# return bin_edges, hist, cumm_number
# #---------------------------------------------------------------------------------
# #-----------------
# #-----------------
# #-----------------
# #---------------------------------------------------------------------------------
# #--- completeness
# mc = 1.5
# #--- t0<t<t1
# #--- set min/max time to avoid temporal incompletenesss issue
# swarm_tmp = swarm.copy()#DataFrameSubSet( swarm,
# # 'date',
# # ( swarm['date'].min(),
# # pd.to_datetime('2010-07-31') ) )
# #--- m > mc
# swarm_lohi = swarm_tmp.copy() #DataFrameSubSet( swarm_tmp,
# # 'magnitude',
# #( mc, sys.maxint ) )
# #--- spatial map
# #swarm_lohi.plot.scatter('longitude','latitude',
# # s=3**(swarm_lohi['magnitude']),
# # c='date',cmap='jet',
# # alpha = 0.4) #--- plot
# #--- temporal map
# #ax1.set_xlim(swarm_tmp['date'].min(),swarm_tmp['date'].max())
# for ii in xrange(10):
# fig = plt.figure(figsize=(8,4))
# ax1=fig.add_subplot(111)
# #plt.xlabel('Time')
# #plt.ylabel('M')
# ax1.set_ylim(0,6)
# tt=swarm[swarm['magnitude']==swarm['magnitude'].sort_values(ascending=False).iloc[ii]]['date'].iloc[0]
# ax1.set_xlim(tt-datetime.timedelta(days=15),tt+datetime.timedelta(days=15))# pd.to_datetime('2014-12-04'),pd.to_datetime('2015-06-1'))
# ax1.tick_params(axis='both',labelsize=18)
# #ax1.tick_params(axis='x',rotation=18)
# ax1.scatter(swarm_lohi['date'],swarm_lohi['magnitude'],
# s=2*np.exp(swarm_lohi['magnitude']),
# alpha=0.04,color='black')
# #--- activity rate
# bin_edges, hist, cumm_number = ActivityRate( swarm_lohi )
# #--- plot
# ax2 = ax1.twinx() # instantiate a second axes that shares the same x-axis
# ax2.plot(pd.to_datetime(bin_edges[:-1]),hist,'r-')
# ax2.tick_params(axis='y',labelsize=18,colors='red')
# ax2.set_yscale('log')
# #ax2.set_ylim(1e1,1e3)
# ax2.xaxis.set_major_formatter(dates.DateFormatter('%b %y'))
# fig.autofmt_xdate()
# fig.savefig('%s/timeSeries_ok.png'%DIR_OUTPT_figs,bbox_inches='tight')
# plt.show()
In [24]:
#--- plot complete catalog
def ConvertDailyRate(hist, bin_edges ):
#---convert data to daily rate
t0 = pd.to_datetime( bin_edges[ 0 ] )
t1 = pd.to_datetime( bin_edges[ 1 ] )
delta_t = ( t1 - t0 ).total_seconds() / ( 60 * 60 )
hist *= ( bin_edges[ 1 ] - bin_edges[ 0 ] ) / delta_t
def ActivityRate( swarm ):
nbins = int( (swarm['date'].max()-swarm['date'].min()).days * 8 ) #--- number of bins
tmax = swarm['date'].max().value #--- min/max
tmin = swarm['date'].min().value
hist, bin_edges = np.histogram(swarm['date'].apply(lambda x:x.value),
bins=np.linspace(tmin,tmax,nbins+1,endpoint=True),density=True) #--- probability dist.
hist *= len( swarm['date'] ) #--- int(hist).dt=n
cumm_number = np.cumsum(hist)*(bin_edges[1]-bin_edges[0]) #--- accumulated number
ConvertDailyRate( hist, bin_edges ) #--- daily activity
return bin_edges, hist, cumm_number
#---------------------------------------------------------------------------------
#-----------------
#-----------------
#-----------------
#---------------------------------------------------------------------------------
#--- completeness
#mc = 1.5
#--- t0<t<t1
myTlohi = Tlohi( pd.to_datetime('2019-07-04'),
pd.to_datetime('2019-07-16')) #swarm['date'].max())
#--- set min/max time to avoid temporal incompletenesss issue
swarm_tmp = DataFrameSubSet( swarm,
'date',
( myTlohi.lo,
myTlohi.hi ) )
#--- m > mc
swarm_lohi = swarm_tmp.copy() #DataFrameSubSet( swarm_tmp,
# 'magnitude',
#( mc, sys.maxint ) )
#--- spatial map
#swarm_lohi.plot.scatter('longitude','latitude',
# s=3**(swarm_lohi['magnitude']),
# c='date',cmap='jet',
# alpha = 0.4) #--- plot
#--- temporal map
fig = plt.figure(figsize=(8,3))#,dpi=150)
ax1=fig.add_subplot(111)
#plt.xlabel('Time')
#plt.ylabel('M')
ax1.set_ylim(0,7.2)
ax1.set_xlim(swarm_tmp['date'].min(),swarm_tmp['date'].max())
ax1.tick_params(axis='both',labelsize=18)
ax1.tick_params(axis='x',rotation=30)
ax1.scatter(swarm_lohi['date'],swarm_lohi['magnitude'],
s=2*np.exp(swarm_lohi['magnitude']),
alpha=0.04,color='black')
DrawFrame(ax1, (0.11,0.07),(0.32,0.1),0.01)
#--- activity rate
bin_edges, hist, cumm_number = ActivityRate( swarm_lohi )
#--- plot
ax2 = ax1.twinx() # instantiate a second axes that shares the same x-axis
ax2.plot(pd.to_datetime(bin_edges[:-1]),hist,'r-',linewidth=1)
ax2.tick_params(axis='y',labelsize=18,colors='red')
#ax2.set_yscale('log')
#ax2.set_ylim(1e1,3e2)
ax2.xaxis.set_major_formatter(dates.DateFormatter('%d %b %y'))
#fig.autofmt_xdate(bottom=.1)
#fig.savefig('%s/timeSeries_ok.png'%DIR_OUTPT_figs,dpi=150,bbox_inches='tight')
plt.show()
In [25]:
#--- evaluate fractal dimension
import geopy.distance
from math import *
import random as rnd
class bins:
def __init__(self, nBin, xlo, xhi, ydim = 1, err = None):
self.lo = xlo - 1.0e-10
self.hi = xhi + 1.0e-10
self.dx = (self.hi-self.lo)/nBin
self.xlist = [0.0 for i in xrange(nBin)]
self.kounter = [0 for i in xrange(nBin)]
self.ylist = [[0.0 for j in xrange(ydim)] for i in xrange(nBin)]
self.nBin = nBin
self.err = err
self.max_y = [[-sys.maxint for j in xrange(ydim)] for i in xrange(nBin) ]
self.min_y = [[sys.maxint for j in xrange(ydim)] for i in xrange(nBin)]
if err:
self.ySQlist = [[0.0 for j in xrange(ydim)] for i in xrange(nBin)]
def GetBin(self,x):
return int(floor((x-self.lo)/self.dx))
def whichBin(self,x,y, ibin=[] ):
assert x >= self.lo, 'x=%s,self.lo=%s'%(10**x,10**self.lo)
assert x < self.hi, 'x=%s,self.hi=%s'%(10**x,10**self.hi)
nr = int(floor((x-self.lo)/self.dx))
if ibin:
ibin[ 0 ] = nr
self.kounter[nr] += 1
self.xlist[nr] += x
for idim in xrange(len(y)):
self.ylist[nr][idim] += y[idim]
if y[idim] >= self.max_y[nr][idim]: #--- set max value
self.max_y[nr][idim]=y[idim]
if y[idim] <= self.min_y[nr][idim]:
self.min_y[nr][idim]=y[idim]
if self.err:
self.ySQlist[nr][idim] += y[ idim ] * y[ idim ]
def res(self, logScaleX = None, logScaleY = None, base = 10, SUM = None, MINMAX=None ):
indices = xrange(10**6)
someList = []
for x,index in zip(self.xlist,indices):
nb = self.kounter[index]
if nb == 0: continue
xbar = self.xlist[index]/nb
ybar = [y/nb for y in self.ylist[index]]
if self.err:
sigmaY = [ ( ysq / nb - YBAR * YBAR ) ** 0.5 / nb ** 0.5 for ysq, YBAR in zip( self.ySQlist[ index ], ybar )]
if SUM:
sigmaY = [ i * nb for i in sigmaY ]
if SUM:
ybar = [y for y in self.ylist[index]]
if MINMAX:
MAX_y = [y for y in self.max_y[index]]
if logScaleX:
xbar = base ** xbar
if logScaleY:
ybar = [ base ** item for item in ybar ]
if self.err:
someList.append([ xbar, ybar, sigmaY ])
elif MINMAX:
someList.append([ xbar, ybar, MAX_y ])
else:
someList.append([ xbar, ybar ])
return someList
class histogram( bins ):
def res( self, Radial = None, logScale = None, normalize = True, base = 10.0, ACCUMLTD = None ):
PDF = []
self.nPoint = nPoint = sum( self.kounter )
indices = xrange( sys.maxint )
y_accm = nPoint
for y, index in zip( self.kounter, indices ):
if not ACCUMLTD and y == 0:
continue
if not y == 0:
x = self.xlist[ index ] / y #self.lo + index * self.dx
else:
x = self.lo + index * self.dx
Y = 1.0 * y
dx = self.dx
if logScale:
x = base ** x
dx = x * ( base ** self.dx - 1.0 )
# print Y, dx
if normalize:
Y /= ( nPoint * dx )
if Radial:
Y /= ( 2.0 * pi * x )
# PDF.append( [ x, Y ] )
# PDF.append( [ x + dx, Y ] )
# PDF.append( [ x + 0.5 * dx, Y, 0.0, ( 1.0 * y_accm / nPoint if normalize else 1.0 * y_accm ) ] )
error_std = 0.0
if self.err:
error_std = sqrt( nPoint * Y * dx ) / ( nPoint * dx ) #--- poisson
error_std = sqrt( nPoint * Y * dx * ( 1.0 - Y * dx ) ) / ( nPoint * dx ) #--- bi-nomial
PDF.append( [ x, Y, 0.0, ( 1.0 * y_accm / nPoint if normalize else 1.0 * y_accm ), error_std ] )
y_accm -= y
return PDF
def GetCartesian( dff ):
df = dff.copy()
xlo = df['longitude'].min()
xhi = df['longitude'].max()
ylo = df['latitude'].min()
yhi = df['latitude'].max()
getDistX = lambda x: geopy.distance.vincenty( ( 0.0, xlo ), ( 0.0, x ) ).km
getDistY = lambda y: geopy.distance.vincenty( ( ylo, 0.0 ), ( y, 0.0 ) ).km
df[ 'x(km)' ] = df[ 'longitude' ].apply( getDistX )
df[ 'y(km)' ] = df[ 'latitude' ].apply( getDistY )
df[ 'z(km)' ] = df['depth']
return df
def fractalDimension2nd( coord ):
#--- sort
if type( coord ) == type( [] ):
coord = ListToDict( coord )
points = coord.keys()
points.sort()
hsObject = histogram( 18 * 8, log( 1e-10,10), log( 1e8, 10 ) )
for point_i in points:
for point_j in points:
if not point_i < point_j: #--- pairs ij with i<j
continue
rij = sum( [ ( i - j ) ** 2 for i, j in zip( coord[ point_i ], coord[ point_j ] ) ] ) # ** 0.5
assert rij > 0, 'rij=%s,coord[ %s ]=%s, coord[ %s ]=%s' %(rij,point_i,coord[ point_i ], point_j, coord[ point_j ] )
hsObject.whichBin( 0.5 * log( rij,10 ), [ 1.0 ] )
for items in hsObject.res( logScale = True, normalize = True, ACCUMLTD = True ):
if items[ 3 ] > 0.0:
yield items[ 0 ], items[ 3 ]
#---------------------------------------------------------------------------------
#-----------------
#-----------------
#-----------------
#---------------------------------------------------------------------------------
mc = 2.0
#--------------------
#----- subset
#--------------------
swarm_lohi = DataFrameSubSet( swarm, #--- complete catalog
'magnitude',
( mc, sys.maxint ) )
swarm_lohi = swarm_lohi.sample( n = 2000 ) #--- sample
#--------------------
#--- cartesian coords
#--------------------
swarm_cartesian = GetCartesian( swarm_lohi )
#--------------------
#--- evaluate df
#--------------------
tmp_coord = swarm_cartesian['x(km)'].apply(lambda x: [x+rnd.random()*1e-6]) +\
swarm_cartesian['y(km)'].apply(lambda x: [x+rnd.random()*1e-6]) +\
swarm_cartesian['z(km)'].apply(lambda x: [x+rnd.random()*1e-6])
tmp_coord = tmp_coord.to_dict()
dict_NR = fractalDimension2nd( tmp_coord ) #, dmin = 1.0e-02 )
#--------------------
#--- scattered plot
#--------------------
swarm_cartesian.plot.scatter('x(km)','y(km)',
s=3**(swarm_lohi['magnitude']),
c='date',cmap='jet',
alpha = 0.4)
#plt.savefig('%s/map2d.png'%DIR_OUTPT_figs,bbox_inches='tight')
#--------------------
#--- N(r) vs r
#--------------------
plt.figure( figsize = (4,4))
plt.xlabel('r(km)')
plt.ylabel('N(r)')
plt.xlim(1e-3,1e2)
plt.ylim(1e-8,1)
plt.yscale('log')
plt.xscale('log')
d_f = 2.2 #1.7
for i in dict_NR:
plt.plot([i[ 0 ]],
[1-i[ 1 ]],
'o',color='black') #--- accumulated
plt.plot(i[ 0 ],
(1-i[ 1 ])/i[0]**d_f,
'.',color='red') #--- accumulated
plt.show()
In [26]:
#--- evaluate fractal dimension (correltion dimension )
def getRmat2d( df_complete ):
nmax = len( df_complete )
rmat = np.matrix(np.zeros(nmax*nmax).reshape(nmax,nmax))
for i in xrange( nmax ):
#--- distance matrix
df_dx = df_complete[ 'x(km)' ] - df_complete[ 'x(km)' ][ i ]
df_dy = df_complete[ 'y(km)' ] - df_complete[ 'y(km)' ][ i ]
df_sq = ( df_dx*df_dx+df_dy*df_dy ) ** 0.5
df_sq[ : i ] = 0
rmat[ i ] = np.array(df_sq)
return np.array( rmat )
def getRmat3d( df_complete ):
nmax = len( df_complete )
rmat = np.matrix(np.zeros(nmax*nmax).reshape(nmax,nmax))
for i in xrange( nmax ):
#--- distance matrix
df_dx = df_complete[ 'x(km)' ] - df_complete[ 'x(km)' ][ i ]
df_dy = df_complete[ 'y(km)' ] - df_complete[ 'y(km)' ][ i ]
df_dz = df_complete[ 'z(km)' ] - df_complete[ 'z(km)' ][ i ]
df_sq = ( df_dx*df_dx+df_dy*df_dy+df_dz*df_dz ) ** 0.5
df_sq[ : i ] = 0
rmat[ i ] = np.array(df_sq)
return np.array( rmat )
#def GetCartesian( dff ):
# df = dff.copy()
# xlo = df['longitude'].min()
# xhi = df['longitude'].max()
# ylo = df['latitude'].min()
# yhi = df['latitude'].max()
# getDistX = lambda x: geopy.distance.vincenty( ( 0.0, xlo ), ( 0.0, x ) ).km
# getDistY = lambda y: geopy.distance.vincenty( ( ylo, 0.0 ), ( y, 0.0 ) ).km
# df[ 'r(km)' ] = df[ 'longitude' ].apply( getDistX ) + df[ 'latitude' ].apply( getDistY ) * 1j
# return df
# --------------------
# ----- subset
# --------------------
swarm_lohi = DataFrameSubSet( swarm, #--- complete catalog
'magnitude',
( mc, sys.maxint ) )
#--------------------
#--- cartesian coords
#--------------------
swarm_lohi = GetCartesian( swarm_lohi )
#swarm_lohi = DataFrameSubSet( swarm_lohi,
# 'x(km)',
# ( 180,300))
#swarm_lohi = DataFrameSubSet( swarm_lohi,
# 'y(km)',
# ( 100,250))
#--- we need the distance matrix!
#rmat2d = getRmat2d( swarm_lohi )
rmat3d = getRmat3d( swarm_lohi )
#r_list2d = rmat2d[rmat2d.nonzero()]
r_list3d = rmat3d[rmat3d.nonzero()]
# #--- histogram
r_min = log(np.min(r_list3d),10) #min(log(np.min(r_list2d),10),log(np.min(r_list3d),10))
r_max = log(np.max(r_list3d),10) #max(log(np.max(r_list2d),10),log(np.max(r_list3d),10))
nbins = int(ceil(r_max - r_min))*4
#2d
hist3d, edges = np.histogram(r_list3d,
bins=np.logspace(r_min, r_max, nbins) )
r_bins, edges = np.histogram(r_list3d,
bins=np.logspace(r_min, r_max, nbins), weights = r_list3d )
r_bins3d = r_bins[hist3d != 0]
hist3d = hist3d[hist3d != 0]
r_bins3d /= hist3d
# #--- normalize
hist_acc_3d = np.cumsum(hist3d)*1.0
hist_acc_3d /= hist_acc_3d[-1]
# #3d
# hist3d, edges = np.histogram(r_list3d,
# bins=np.logspace(r_min, r_max, nbins) )
# r_bins, edges = np.histogram(r_list3d,
# bins=np.logspace(r_min, r_max, nbins), weights = r_list3d )
# r_bins3d = r_bins[hist3d != 0]
# hist3d = hist3d[hist3d != 0]
# r_bins3d /= hist3d
# #--- normalize
# hist_acc_3d = np.cumsum(hist3d)*1.0
# hist_acc_3d /= hist_acc_3d[-1]
##--------------------
##--- scattered plot
##--------------------
#plt.scatter(swarm_lohi['x(km)'],
# swarm_lohi['y(km)'],
# s=3**(swarm_lohi['magnitude']),
# cmap='jet',
# alpha = 0.1)
#
##--- plot
##d_f = 1.4
#fig = plt.figure(figsize=(4,4))
#ax = fig.add_subplot(111)
#ax.set_xlim(10**r_min,10**r_max)
#ax.set_xlabel('$r(km)$')
#ax.set_ylabel('$N(r)$')
#ax.set_xscale('log')
#ax.set_yscale('log')
#ax.errorbar( r_bins, hist_acc,
# yerr = hist_acc/hist**.5,
# color='black',marker='o')
#
#ax.errorbar( r_bins, 10000*hist_acc/r_bins**d_f, #--- rescaled
# yerr = hist_acc/hist**.5/r_bins**d_f,
# color='red',marker='o',label='$N/r^{%s}$'%d_f)
#ax.legend()
#
#fig.savefig('%s/corrDim.png'%DIR_OUTPT_figs,bbox_inches='tight')
In [27]:
#--- plot
d_f = 2.1 #1.7
fig = plt.figure(figsize=(4,4))
ax = fig.add_subplot(111)
ax.axis([1e-5,1e3,1e-8,1e0])
ax.set_xlabel('$r(km)$')
ax.set_ylabel('$N(r)$')
ax.set_xscale('log')
ax.set_yscale('log')
ax.errorbar( r_bins3d, hist_acc_3d,
yerr = hist_acc_3d/hist3d**.5,
color='black',marker='o')
# ax.errorbar( r_bins3d, hist_acc_3d,
# yerr = hist_acc_3d/hist3d**.5,
# color='red',marker='s')
#ax.errorbar( r_bins, 10000*hist_acc/r_bins**d_f, #--- rescaled
# yerr = hist_acc/hist**.5/r_bins**d_f,
# color='red',marker='o',label='$N/r^{%s}$'%d_f)
ax.plot(r_bins3d, r_bins3d**d_f,
'-.r',label='$r^{%s}$'%d_f)
ax.legend()
#fig.savefig('%s/corrDim.png'%DIR_OUTPT_figs,bbox_inches='tight')
plt.show()
In [28]:
#--- evaluate fractal dimension (box counting )
import geopy.distance
from math import *
import random as rnd
#import warnings
#warnings.filterwarnings('ignore') #--- get rid of warnings
#def GetCartesian( dff ):
# df = dff.copy()
# xlo = df['longitude'].min()
# xhi = df['longitude'].max()
# ylo = df['latitude'].min()
# yhi = df['latitude'].max()
# getDistX = lambda x: geopy.distance.vincenty( ( 0.0, xlo ), ( 0.0, x ) ).km
# getDistY = lambda y: geopy.distance.vincenty( ( ylo, 0.0 ), ( y, 0.0 ) ).km
# df[ 'r(km)' ] = df[ 'longitude' ].apply( getDistX ) + df[ 'latitude' ].apply( getDistY ) * 1j
# df[ 'x(km)' ] = df[ 'longitude' ].apply( getDistX )
# df[ 'y(km)' ] = df[ 'latitude' ].apply( getDistY )
# return df
#--------------------
#----- subset
#--------------------
# swarm_lohi = DataFrameSubSet( swarm, #--- complete catalog
# 'magnitude',
# ( mc, sys.maxint ) )
# #swarm_lohi = swarm_lohi.sample( n = 1000 ) #--- sample
# #--------------------
# #--- cartesian coords
# #--------------------
# swarm_lohi = GetCartesian( swarm_lohi )
# #swarm_lohi = DataFrameSubSet( swarm_lohi, #--- complete catalog
# # 'x(km)',
# # ( 200, 1000 ) )
# #swarm_lohi = DataFrameSubSet( swarm_lohi, #--- complete catalog
# # 'y(km)',
# # ( -1000, 220 ) )
# #--------------------
# #--- scattered plot
# #--------------------
# plt.figure(figsize=(4,4))
# #plt.xlim(0,np.max(r_list))
# #plt.ylim(-np.max(r_list)/2,np.max(r_list)/2)
# plt.xlabel('x(km)')
# plt.ylabel('z(km)')
# plt.scatter(swarm_lohi['x(km)'],
# swarm_lohi['z(km)'],
# s=3**(swarm_lohi['magnitude']),
# cmap='jet',
# alpha = 0.01)
# #--------------------
# #--- box counting
# #--------------------
# #tmp=pd.DataFrame({'x(m)':swarm_lohi['y(m)'],'y(m)':swarm_lohi['z(m)']}) #,'z(m)':swarm_lohi['z(m)']})
# #rmat = getRmat2d( tmp )
# #rmat = getRmat2d( swarm_lohi )
# #r_list = rmat[rmat.nonzero()]
# #r_min = np.min(r_list)
# #r_max = np.max(r_list)
# #
# plt.savefig('%s/map2d.png'%DIR_OUTPT_figs,bbox_inches='tight')
In [29]:
# #--- evaluate fractal dimension (box counting )
# def fractalDimension3d( x, y, z, L, dmin = None ):
# x = np.array(x)
# y=np.array(y)
# z=np.array(z)
# # xlo = x.min()
# # xhi = x.max()
# # ylo = y.min()
# # yhi = y.max()
# # zlo = z.min()
# # zhi = z.max()
# # L = max( zhi - zlo, yhi - ylo, xhi - xlo )
# #---
# xc = x.mean() #--- center
# yc = y.mean()
# zc = z.mean()
# xo = xc - L #--- origin
# yo = yc - L
# zo = zc - L
# # L *= 2.0
# #---
# kounter = 0 #--- number of divisions
# dx = dy = dz = L #--- scale
# dl = []
# N = []
# while dx - dmin > 0.0: #--- do until dx < dmin
# d = {}
# index_i = np.array( map(int,np.floor( ( y - yo ) / dy ) ) )
# index_j = np.array( map( int, np.floor( ( x - xo ) / dx ) ) )
# index_k = np.array( map( int, np.floor( ( z - zo ) / dz ) ) )
# inside_cell_lo = np.all([index_i>=0,index_j>=0,index_k>=0.0],axis=0) #--- point is inside?
# inside_cell_hi = np.all([index_i<2**kounter,index_j<2**kounter,index_k<2**kounter],axis=0) #
# inside_cell = np.all([inside_cell_lo,inside_cell_hi],axis = 0)
# cell_id = index_k * 4 ** kounter + index_i * ( 2**kounter ) + index_j
# #---
# dl+=[dx]
# N+=[len( set( cell_id ) )]
# #---
# kounter += 1
# dx = dy = dz = L / 2**kounter
# assert dx - dmin <= 0.0
# #---
# return np.array(dl), np.array(N)
# def fractalDimension2d( x, y, L, dmin = None ):
# x = np.array(x)
# y=np.array(y)
# # xlo = x.min()
# # xhi = x.max()
# # ylo = y.min()
# # yhi = y.max()
# # L = max( yhi - ylo, xhi - xlo )
# #---
# xc = x.mean() #--- center
# yc = y.mean()
# xo = xc - L #--- origin
# yo = yc - L
# # L *= 2.0
# #---
# kounter = 0 #--- number of divisions
# dx = dy = L / 2**kounter #--- scale
# dl = []
# N = []
# # pdb.set_trace()
# # fig = plt.figure(figsize=(4,4))
# # ax=fig.add_subplot(111)
# # plt.scatter(x,y)
# # ax.add_patch( patches.Rectangle(xy=(xo,yo), width=L,
# # height=L, linewidth=1,
# # clip_on=False,facecolor=None,edgecolor='black',fill=None) )
# while dx - dmin > 0.0: #--- do until dx < dmin
# d = {}
# index_i = np.array( map(int,np.floor( ( y - yo ) / dy ) ) ) #--- assingn index
# index_j = np.array( map( int, np.floor( ( x - xo ) / dx ) ) )
# inside_cell_lo = np.all([index_i>=0,index_j>=0],axis=0) #--- point is inside?
# inside_cell_hi = np.all([index_i<2**kounter,index_j<2**kounter],axis=0) #
# inside_cell = np.all([inside_cell_lo,inside_cell_hi],axis = 0)
# index_i = index_i[ inside_cell ] #--- subset of the index array
# index_j = index_j[ inside_cell ]
# cell_id = index_i * ( 2**kounter ) + index_j
# #---
# dl+=[dx]
# N+=[len( set( cell_id ) )]
# #---
# kounter += 1
# dx = dy = L / 2**kounter
# assert dx - dmin <= 0.0
# #---
# return np.array(dl), np.array(N)
# fig = plt.figure(figsize=(10,4))
# ax = fig.add_subplot(121)
# ax2 = fig.add_subplot(122)
# ax.set_xlabel('$r(km)$')
# ax.set_ylabel('$N(r)$')
# ax.set_xscale('log')
# ax.set_yscale('log')
# ax2.set_xlabel('$r(km)$')
# ax2.set_ylabel(r'$N(r)\times r^{%s}$'%d_f)
# ax2.set_xscale('log')
# ax2.set_yscale('log')
# dl={}
# N={}
# count = 0
# r_min = np.min(r_list)
# r_max = np.max(r_list)
# for L in np.logspace(log(r_min,2),log(r_max,2),num=6,base=2.0):
# #for L in [2*420.0]:
# # dl[count], N[count] = fractalDimension2d( swarm_lohi['x(km)'],
# # swarm_lohi['y(km)'], L, dmin=r_min ) # , swarm_lohi['z(m)'], dmin=r_min )
# dl[count], N[count] = fractalDimension3d( swarm_lohi['x(km)'],
# swarm_lohi['y(km)'],
# swarm_lohi['z(km)'],
# L, dmin=r_min )
# ##--- try random
# #x=np.array([rnd.random() for i in xrange(1000)])
# #y=0.2*x #[rnd.random() for i in xrange(10000)]
# ##z=x #[rnd.random() for i in xrange(10000)]
# #tmp=pd.DataFrame({'x(m)':x,'y(m)':y})#,'z(m)':z})
# #rmat = getRmat2d( tmp )
# #r_list = rmat[rmat.nonzero()]
# #r_min = min(r_list)
# #sdict = fractalDimension2d( x,y,
# # dmin=r_min )
# #plt.scatter(x,y)
# #-- plot
# #ax.set_xlim(10**r_min,10**r_max)
# #for key in sdict:
# ax.plot(dl[count],N[count],'-o')
# ax2.plot(dl[count],N[count]*dl[count]**d_f,marker='o',label='$L=%2.1e$'%L)#,linestyle='None')
# count+=1
# ax2.legend(bbox_to_anchor=(1, 1))
# fig.tight_layout()
# fig.savefig('%s/boxCount.png'%DIR_OUTPT_figs,bbox_inches='tight')
In [30]:
Df = 2.1 #1.7 #2.2 #2.0 #1.7
bval = 0.8
mc=2.0 #1.5
In [31]:
#--- trig analysis (new) (it's a large data sets. run the simulation on a cluster and use the outputs)
from scipy.sparse import lil_matrix
import time
from IPython.display import display
import datetime
import pdb
import numpy.linalg
import numpy as np
def UpperTriang(a):
il1 = np.tril_indices(a.shape[0])
a[il1] = 0
return a
def getTmat( df_complete ):
nmax = len( df_complete )
prefact = 1.0 / ( 24.0 * 60 * 60 ) #--- daily
tmat = np.matrix(np.zeros(nmax*nmax).reshape(nmax,nmax))
tmat_ut = np.matrix(np.zeros(nmax*nmax).reshape(nmax,nmax))
for i in xrange( nmax ):
df_dt = ( df_complete[ 'date' ] - df_complete[ 'date' ][ i ] ).dt.total_seconds() * prefact #--- time diff between i-th event and all subsequent events
tmat[ i ] = np.array(df_dt)
df_dt[ : i ] = df_dt[ i ] #--- must have an upper triangular matrix
tmat_ut[ i ] = np.array(df_dt)
#---
return np.array( tmat ), np.array( tmat_ut )
def AddPositionList(df_complete):
df_complete['r(m)'] = df_complete['x(m)'].apply(lambda x: [x])+ \
df_complete['y(m)'].apply(lambda x: [x])+ \
df_complete['z(m)'].apply(lambda x: [x])
def getRmat( df_complete ):
nmax = len( df_complete )
rmat = np.matrix(np.zeros(nmax*nmax).reshape(nmax,nmax))
rmat_ut = np.matrix(np.zeros(nmax*nmax).reshape(nmax,nmax))
for i in xrange( nmax ):
#--- distance matrix
df_dx = ( df_complete[ 'x(km)' ] - df_complete[ 'x(km)' ][ i ] )
df_dy = ( df_complete[ 'y(km)' ] - df_complete[ 'y(km)' ][ i ] )
df_dz = ( df_complete[ 'z(km)' ] - df_complete[ 'z(km)' ][ i ] ) #comment if 2-d
df_sq = ( df_dx * df_dx + df_dy * df_dy + df_dz * df_dz ) ** 0.5
rmat[ i ] = np.array(df_sq)
df_sq[ : i ] = 0
rmat_ut[ i ] = np.array(df_sq)
return np.array( rmat ), np.array( rmat_ut )
def getMmat( df_complete ):
nmax = len( df_complete )
m_mat = np.matrix(np.zeros(nmax*nmax).reshape(nmax,nmax))
m_mat_ut = np.matrix(np.zeros(nmax*nmax).reshape(nmax,nmax))
for i in xrange( nmax ):
#--- magnitude
df_m = pd.Series( [ df_complete[ 'magnitude' ][ i ] ] * nmax )
m_mat[ i ] = np.array(df_m)
df_m[ : i ] = 0
m_mat_ut[ i ] = np.array(df_m)
return np.array( m_mat ), np.array( m_mat_ut )
def vectorizedAnalysis( df_complete ):
#--- setup t, r, m
t0 = time.time()
tmat0, tmat = getTmat( df_complete )
print 'setting up tmat:%s s'%(time.time() - t0)
t0 = time.time()
r_mat0, r_mat = getRmat( df_complete )
print 'setting up rmat:%s s'%(time.time() - t0)
t0 = time.time()
m_mat0, m_mat = getMmat( df_complete )
print 'setting up m_mat:%s s'%(time.time() - t0)
# #--- make upper-triangular matrices
# t0 = time.time()
# tmat = UpperTriang(np.copy(tmat0))
# r_mat = UpperTriang(np.copy(r_mat0))
# m_mat = UpperTriang(np.copy(m_mat0))
# print 'setting up ut matrix:%s s'%(time.time() - t0)
#--- nij
t0 = time.time()
NIJ = tmat * r_mat ** ( Df ) * 10 ** ( - bval * ( m_mat - mc ) )
TIJ = tmat * 10 ** ( - 0.5 * bval * ( m_mat - mc ) ) #--- scaled time
RIJ = NIJ / TIJ #r_mat ** ( Df ) * 10 ** ( - 0.5 * bval * ( m_mat - mc ) ) #--- scaled time
print 'setting up NIJ:%s s'%(time.time() - t0)
nmax = len( df_complete )
N_sparse = lil_matrix( ( nmax, nmax ) ) #--- sparse matrix
T_sparse = lil_matrix( ( nmax, nmax ) )
R_sparse = lil_matrix( ( nmax, nmax ) )
for junk, j in zip( NIJ, xrange( sys.maxint ) ):
if j == 0:
continue
x = min( NIJ[ : j, j ][ NIJ[ : j, j ] != 0 ] ) #--- min nij
assert x != 0.0
rowi = np.where( NIJ[ : j, j ] == x )[ 0 ][ 0 ] #--- find row
assert rowi <= j
N_sparse[ rowi, j ] = x #--- insert
T_sparse[ rowi, j ] = TIJ[ rowi, j ]
R_sparse[ rowi, j ] = RIJ[ rowi, j ]
return N_sparse, (T_sparse, tmat0 ), ( R_sparse, r_mat0 ), m_mat0
#--------------------
#----- subset
#--------------------
#--- t0<t<t1
# myTlohi = Tlohi( pd.to_datetime('2019-07-04'),
# swarm['date'].max())
# swarm_lohi = DataFrameSubSet( swarm, #--- complete catalog
# 'date',
# ( myTlohi.lo, myTlohi.hi ) )
swarm_lohi = DataFrameSubSet( swarm, #--- complete catalog
'magnitude',
( mc, sys.maxint ) )
swarm_lohi.reset_index(inplace=True,drop=True)
#--------------------
#--- cartesian coords
#--------------------
swarm_lohi = GetCartesian( swarm_lohi )
#AddPositionList( swarm_lohi )
swarm_lohi.reset_index(inplace=True,drop=True)
#--- vectorized
t0 = time.time()
N_sparse, (T_sparse,tmat), (R_sparse,rmat), m_mat = vectorizedAnalysis( swarm_lohi )
print 'duration=%s s'%(time.time() - t0)
In [32]:
# #--- random analysis
# def shuffle(amat):
# ind_list = range(amat.shape[0])
# np.random.shuffle(ind_list)
# amat_row = amat[ind_list]
# return amat_row[:,ind_list]
# def GetNij(rmat,tmat,m_mat,df_complete):
# tmat = shuffle(np.abs(tmat))
# r_mat = shuffle(rmat)
# m_mat = shuffle(m_mat)
# #--- nij
# NIJ = tmat * r_mat ** ( Df ) * 10 ** ( - bval * ( m_mat - mc ) )
# TIJ = tmat * 10 ** ( - 0.5 * bval * ( m_mat - mc ) ) #--- scaled time
# RIJ = r_mat ** ( Df ) * 10 ** ( - 0.5 * bval * ( m_mat - mc ) ) #--- scaled time
# nmax = len( df_complete )
# N_sparse = lil_matrix( ( nmax, nmax ) ) #--- sparse matrix
# T_sparse = lil_matrix( ( nmax, nmax ) )
# R_sparse = lil_matrix( ( nmax, nmax ) )
# for junk, j in zip( NIJ, xrange( sys.maxint ) ):
# if j == 0:
# continue
# x = min( NIJ[ : j, j ][ NIJ[ : j, j ] != 0 ] ) #--- min nij
# assert x != 0.0
# rowi = np.where( NIJ[ : j, j ] == x )[ 0 ][ 0 ] #--- find row
# N_sparse[ rowi, j ] = x #--- insert
# T_sparse[ rowi, j ] = TIJ[ rowi, j ]
# R_sparse[ rowi, j ] = RIJ[ rowi, j ]
# return N_sparse, (T_sparse, tmat ), ( R_sparse, r_mat), m_mat
# N_sparse_rnd = {}
# T_sparse_rnd = {}
# R_sparse_rnd = {}
# tmat_rnd = {}
# rmat_rnd = {}
# nsamp = 1
# tmat = np.abs(tmat)
# for i in xrange(nsamp):
# print i
# N_sparse_rnd[i], (T_sparse_rnd[i],tmat_rnd[i]), (R_sparse_rnd[i],rmat_rnd[i]), junk = GetNij(rmat,tmat,m_mat,swarm_lohi)
random analysis¶
In [33]:
#--- random analysis 1st
def shuffleDIC( dataFrame, column = None, seed=None ):
junk=dataFrame[column].sample(frac=1,random_state=seed).reset_index(drop=True)
dataFrame[column] = np.array(junk)
def shuffle(df, n=1, axis=0):
df = df.copy()
for _ in range(n):
df.apply(np.random.shuffle, axis=axis)
return df
def AssignXYZ(AssignXYZ):
swarm_shuffled['x(m)'] = swarm_shuffled['r(m)'].apply(lambda x:x.real)
swarm_shuffled['y(m)'] = swarm_shuffled['r(m)'].apply(lambda x:x.imag)
#--------------------
#--- randomize
#--------------------
swarm_shuffled = swarm_lohi.copy()
#AddPositionList( swarm_shuffled )
#display(swarm_shuffled.head())
shuffleDIC( swarm_shuffled, column = 'magnitude', seed=64*4)
shuffleDIC( swarm_shuffled, column = ['x(km)','y(km)','z(km)'], seed=128*32)
display(swarm_shuffled.head())
#AssignXYZ(AssignXYZ)
#swarm_shuffled.to_csv('%s/swarm_shuffled_incomplete.csv'%DIR_OUTPT) #--- store
if 1: #not LOAD_MAT:
#--------------------
#--- vectorized
#--------------------
t0 = time.time()
N_sparse_rnd, (T_sparse_rnd, tmat_rnd), (R_sparse_rnd,rmat_rnd), junk = vectorizedAnalysis( swarm_shuffled)
print 'analysis duration=%s s'%(time.time() - t0)
#--------------------
#--- save sparse
#--------------------
# for mat, title in zip([N_sparse_rnd,T_sparse_rnd,R_sparse_rnd],
# ['N_sparse_rnd_matrix.npz','T_sparse_rnd_matrix.npz','R_sparse_rnd_matrix.npz']):
# scipy.sparse.save_npz('%s/%s'%(DIR_OUTPT,title), mat.tocsr()) #--- output
# swarm_shuffled.to_csv('%s/swarm_shuffled.csv'%DIR_OUTPT)
#else: #--- load previously-computed matrices
# N_sparse_rnd = scipy.sparse.load_npz('%s/N_sparse_rnd_matrix.npz'%DIR_OUTPT )
# T_sparse_rnd = scipy.sparse.load_npz('%s/T_sparse_rnd_matrix.npz'%DIR_OUTPT )
# R_sparse_rnd = scipy.sparse.load_npz('%s/R_sparse_rnd_matrix.npz'%DIR_OUTPT )
# swarm_shuffled = pd.read_csv('%s/swarm_shuffled.csv'%DIR_OUTPT)
# swarm_shuffled_incomplete = pd.read_csv('%s/swarm_shuffled_incomplete.csv'%DIR_OUTPT)
In [34]:
# #--- save sparse matrices
# import scipy.sparse
# for mat, title in zip([N_sparse,T_sparse,R_sparse],
# ['N_sparse_matrix.npz','T_sparse_matrix.npz','R_sparse_matrix']):
# scipy.sparse.save_npz('%s/%s'%(DIR_OUTPT,title), mat.tocsr()) #--- output
# for mat, title in zip([N_sparse_rnd[0],T_sparse_rnd[0],R_sparse_rnd[0]],
# ['N_sparse_rnd_matrix.npz','T_sparse_rnd_matrix.npz','R_sparse_rnd_matrix']):
# scipy.sparse.save_npz('%s/%s'%(DIR_OUTPT,title), mat.tocsr()) #--- output
# #swarm_shuffled.to_csv('%s/swarm_shuffled.csv'%DIR_OUTPT)
In [35]:
# #--- load sparse matrices
# #--- 1- run on the cluster:
# #--- 2- sbatch --mem=8gb --partition=single --time=02:59:59 -n 1 ./oarScript.sh
# #--- 3- oarScript.sh: source activate conda-env; python ./swarmEMC.py
# #--- 4- copy: scp arc:/home/kamran.karimi1/Project/seismic/dataset/El_Mayor_Cucpah/* ./swarm/dataset/El_Mayor_Cucpah/
# import scipy.sparse
# DIR_OUTPT0 = './runRidgeCrest/Run0'
# N_sparse = scipy.sparse.load_npz('%s/N_sparse_matrix.npz'%DIR_OUTPT0 )
# T_sparse = scipy.sparse.load_npz('%s/T_sparse_matrix.npz'%DIR_OUTPT0 )
# R_sparse = scipy.sparse.load_npz('%s/R_sparse_matrix.npz'%DIR_OUTPT0 )
# #rmat = np.load('%s/rmat.npy'%DIR_OUTPT)
# #tmat = np.load('%s/tmat.npy'%DIR_OUTPT)
# N_sparse_rnd = {}
# T_sparse_rnd = {}
# R_sparse_rnd = {}
# nsamp = 1
# N_sparse_rnd[0] = scipy.sparse.load_npz('%s/N_sparse_rnd_matrix.npz'%DIR_OUTPT0 )
# T_sparse_rnd[0] = scipy.sparse.load_npz('%s/T_sparse_rnd_matrix.npz'%DIR_OUTPT0 )
# R_sparse_rnd[0] = scipy.sparse.load_npz('%s/R_sparse_rnd_matrix.npz'%DIR_OUTPT0 )
# #rmat_rnd = np.load('%s/rmat_rnd.npy'%DIR_OUTPT)
# #tmat_rnd = np.load('%s/tmat_rnd.npy'%DIR_OUTPT)
# #swarm_shuffled = pd.read_csv('%s/swarm_shuffled.csv'%DIR_OUTPT)
# #swarm_shuffled_incomplete = pd.read_csv('%s/swarm_shuffled_incomplete.csv'%DIR_OUTPT)
In [36]:
##--- matrix map of nij & nij_rand
#
#plt.subplot(2,1,1)
#plt.pcolormesh(np.log(N_sparse.toarray()),cmap='jet')
#plt.subplot(2,1,2)
#plt.pcolormesh(np.log(N_sparse_rnd.toarray()),cmap='jet')
In [37]:
# mpl.rcParams.update(mpl.rcParamsDefault)
# warnings.filterwarnings('ignore') #--- get rid of warnings
# rc('text', usetex=True)
# font = {'size' : 26}
# matplotlib.rc('font', **font)
#---------------------------
#--- compute threshold n_th
#---------------------------
def PLOT(edges, hist, cdf, title ):
#--- plot
plt.figure(figsize=(8,4))
plt.subplot(1,2,1)
# plt.xlim(1e-13,1)
# plt.ylim(1e-1,1e13)
plt.xscale('log')
plt.yscale('log')
plt.xlabel('nij')
plt.ylabel('P(nij)')
plt.title( title )
plt.plot(edges[:-1],hist,'.-')
plt.subplot(1,2,2)
# plt.xlim(1e-13,1)
# plt.ylim(1e-3,1)
plt.xscale('log')
plt.yscale('log')
plt.xlabel('nij')
plt.ylabel('cdf')
plt.plot(edges[:-1],cdf,'.-')
plt.plot([n_thresh for i in edges[:-1]], cdf)
#---
def HIST( nij, nbins ):
#--- histograms
nij_TxR = nij['T*']*nij['R*']
hist, edges = np.histogram( nij_TxR,
bins=np.logspace(np.log(nij_TxR.min()),np.log(nij_TxR.max()),nbins),
density=True)
#--- accumulated
cdf, edges = np.histogram( nij_TxR,
bins=np.logspace(np.log(nij_TxR.min()),np.log(nij_TxR.max()),nbins,endpoint=True))
cdf=np.cumsum(cdf)
#assert cdf[-1] == len(nij_TxR), '%s,%s'%(cdf[-1], len(nij_TxR))
N = 1.0 * len(nij_TxR)
cdf = cdf / N
return edges, hist, cdf
def reset_xticks(nn,ax,(TMIN,TMAX)):
ax.set_xticks( np.linspace(ax.axis()[0],ax.axis()[1],nn) )
labels=np.linspace(TMIN,TMAX,nn)
labels = [r'$10^{%i}$'%i for i in labels]
ax.set_xticklabels(labels)
def reset_yticks(nn,ax,(RMIN,RMAX)):
ax.set_yticks( np.linspace(ax.axis()[2],ax.axis()[3],nn) )
labels=np.linspace(RMIN,RMAX,nn)
labels = [r'$10^{%i}$'%i for i in labels]
ax.set_yticklabels(labels)
def GetTrigListLoHi( nij_trig, col, (tlo,thi), swarm_lohi ):
list_of_mothers = nij_trig.groupby(by='Parent_id').groups.keys()
list_of_mothers.sort()
tmp_df = swarm_lohi.loc[ list_of_mothers ]
tmp_df = tmp_df[ (tmp_df[ col ] >= tlo) &
(tmp_df[ col ] < thi) ]
return nij_trig[ pd.DataFrame([nij_trig['Parent_id'] == i for i in tmp_df.index]).any() ]
def GetInterpolatedData( df0, (TMIN,TMAX),(RMIN,RMAX) ):
nbins_per_decade = 16
nbins_x=nbins_y=int(TMAX-TMIN)*nbins_per_decade
df=df0.copy()
df['T*']=df[ 'T*' ].apply(lambda x: log(x,10))
df['R*']=df[ 'R*' ].apply(lambda x: log(x,10))
heatmap, xedges, yedges = np.histogram2d( df[ 'T*' ], df[ 'R*'], bins=[np.linspace(TMIN,TMAX,nbins_x+1), np.linspace(RMIN,RMAX,nbins_y+1)], normed=True)
heatmap *= len( df )
heatmap = gaussian_filter( heatmap, sigma = nbins_per_decade/4 )
return heatmap
def GetDistance( df1, df2 ):
df_sq = (np.array( df1['x(km)'] ) - np.array( df2['x(km)'] ) ) ** 2 + \
(np.array( df1['y(km)'] ) - np.array( df2['y(km)'] ) ) ** 2 + \
(np.array( df1['z(km)'] ) - np.array( df2['z(km)'] ) ) ** 2
return pd.Series( df_sq ** 0.5 )
def RemovePair( dff, cs, catalog ):
pref = 1.0 / 3600.0 / 24 #--- daily
df = dff.copy()
series_r = GetDistance(catalog.loc[df['Parent_id']],catalog.loc[df['Event_id']])
# series_r = pd.Series(np.array( catalog.loc[df['Parent_id']]['r(km)'] ) -\
# np.array( catalog.loc[df['Event_id']]['r(km)'] ) )
assert len(series_r[series_r==np.nan]) == 0
df['R'] = series_r.copy() #abs()
series_t = pd.Series(np.array( catalog.loc[df['Event_id']]['date'] ) -\
np.array( catalog.loc[df['Parent_id']]['date'] ) )
df['T'] = series_t.apply(lambda x:x.total_seconds()*pref)
assert len ( df[ df['R'] == 0.0 ] ) == 0, '%s'%display( df[ df['R'] == 0.0 ] )
assert len ( df[ df['T'] == 0.0 ] ) == 0, '%s'%display( df[ df['T'] == 0.0 ] )
return df [ df[ 'R' ] <= df[ 'T' ] * cs ], df [ df[ 'R' ] > df[ 'T' ] * cs ]
#--------------------
#----- set parameters
#--------------------
#--- set quantile
quantile = 0.13 #kam 0.5 #0.35 #--- comment if passed by argument
#--- wave speed
cs = 3 * (24*3600) #--- km per day
#--- cut-off time
dt_cut = 0.0 #--- day
#--- plot scattered
# TMIN=-5
# TMAX=3
# RMIN=-4
# RMAX=4
#--------------------
#----- subset (the same as trig. analysis)
#--------------------
#--- t0<t<t1
# myTlohi = Tlohi( pd.to_datetime('2019-07-04'),
# swarm['date'].max())
# swarm_lohi = DataFrameSubSet( swarm, #--- complete catalog
# 'date',
# ( myTlohi.lo, myTlohi.hi ) )
swarm_lohi = DataFrameSubSet( swarm, #--- complete catalog
'magnitude',
( mc, sys.maxint ) )
swarm_lohi.reset_index(inplace=True,drop=True)
#--------------------
#--- cartesian coords
#--------------------
swarm_lohi = GetCartesian( swarm_lohi )
#AddPositionList( swarm_lohi )
swarm_lohi.reset_index(inplace=True,drop=True)
#--------------------
#--- store actual data in a dataframe
#--------------------
rows, cols = N_sparse.nonzero()
tlist = T_sparse[rows, cols].toarray()[0]
rlist = R_sparse[rows, cols].toarray()[0]
nij = pd.DataFrame({'Event_id':cols, 'Parent_id':rows,'T*':tlist,'R*':rlist})
#--------------------
#--- store random data in a dataframe
#--------------------
#nij_rnd = {}
for i in xrange(1): #nsamp):
rows, cols = N_sparse_rnd.nonzero()
tlist = T_sparse_rnd[rows, cols].toarray()[0]
rlist = R_sparse_rnd[rows, cols].toarray()[0]
nnn = len(cols)
nij_rnd = pd.DataFrame({'Event_id':cols, 'Parent_id':rows,'T*':tlist,'R*':rlist},index=range(i*nnn,(i+1)*nnn))
#--------------------------------------------
#----- only include mother events with
#----- t_mother between (t_lo, t_hi)
#--------------------------------------------
#--- actual data
#--- remove pairs with r > cs.t
nij, nij_removed = RemovePair( nij, cs, swarm_lohi )
myTlohi = Tlohi(swarm_lohi['date'].min()+datetime.timedelta(days=dt_cut), #--- set cut-off time
swarm_lohi['date'].max()+datetime.timedelta(days=-dt_cut)
)
nij = GetTrigListLoHi( nij, 'date', #--- t_mother > t_lo
( myTlohi.lo, myTlohi.hi ),
swarm_lohi)
nij.reset_index(inplace=True, drop=True)
#--- random data
#for i in xrange(nsamp):
# nij_rnd = RemovePair( nij_rnd, cs, swarm_shuffled )
# nij_rnd = GetTrigListLoHi( nij_rnd, 'date',
# ( myTlohi.lo, myTlohi.hi ),
# swarm_shuffled)
# nij_rnd.reset_index(inplace=True, drop=True)
#--- compute threshold
N_thresh = []
frames = []
for i in xrange(1): #nsamp):
frames.append(nij_rnd)
#--- plot histograms for random data
edges, hist, cdf = HIST( nij_rnd, 1024 )
# edges = 0.5*(edges[:-1]+edges[1:])
N_thresh.append(edges[:-1][cdf>quantile][0])
#n_thresh = np.mean(N_thresh) #--- comment if passed by arg.
print 'n_th=%2.1e+%2.1e' %(n_thresh,np.std(N_thresh) / nsamp ** 0.5)
Nij_rnd = pd.concat([nij_rnd]) #frames)
#--- distribution of nij (actual data)
edges_actual, hist_actual, cdf_actual = HIST( nij, 1024 )
#edges_actual = 0.5*(edges_actual[:-1]+edges_actual[1:])
#PLOT(edges, hist, cdf, 'random')
#--- (Tmin,Tmax)-(Rmin,Rmax)
TMIN=np.floor(np.log10(nij['T*']).min())
TMAX=np.ceil(np.log10(nij['T*']).max())
RMIN=np.floor(np.log10(nij['R*']).min())
RMAX=np.ceil(np.log10(nij['R*']).max())
#--------------------
#--- plot scattered
#--------------------
fig = plt.figure(figsize=(8,4))
#--------------------
#--- interpolated data
#--------------------
for nn, index, title in zip([ nij, Nij_rnd ],xrange(2),['actual','randomized']):
#for nn, index, title in zip([ nij ],xrange(2),['actual']):
ax = fig.add_subplot(1,2,index+1)
#--- interpolate
heatmap=GetInterpolatedData(nn,(TMIN,TMAX),(RMIN,RMAX))
ax.pcolormesh(heatmap.T,cmap='coolwarm')
#---
# ax.set_xlabel('T*')
# ax.set_ylabel('R*')
# ax.set_title(title)
##--- reset x-ticks
reset_xticks(4,ax,(TMIN,TMAX))
#--- reset y-ticks
reset_yticks(4,ax,(RMIN,RMAX))
#--- nij must be within limits
nij_copy = nn.copy()
nij_copy=nij_copy[(nij_copy['T*'] >= 10**TMIN ) &
(nij_copy['T*'] < 10**TMAX ) &
(nij_copy['R*'] >= 10**RMIN ) &
(nij_copy['R*'] < 10**RMAX )]
#--- mapping
xx=ax.axis()[0]+(ax.axis()[1]-ax.axis()[0])*(np.log10(nij_copy['T*'])-TMIN)/(TMAX-TMIN)
yy=ax.axis()[2]+(ax.axis()[3]-ax.axis()[2])*(np.log10(nij_copy['R*'])-RMIN)/(RMAX-RMIN)
ax.set_xlim(ax.axis()[0],ax.axis()[1])
ax.set_ylim(ax.axis()[2],ax.axis()[3])
#--- plot
DrawFrame(ax, (0.25,0.08),(0.16,0.08),0.01)
ax.scatter(xx,
yy,
alpha=1,color='black',s=0.01)
#--- draw the separation line
xx=ax.axis()[0]+(ax.axis()[1]-ax.axis()[0])*(np.log10(nij_copy['T*'])-TMIN)/(TMAX-TMIN)
yy=ax.axis()[2]+(ax.axis()[3]-ax.axis()[2])*(np.log10(n_thresh/nij_copy['T*'])-RMIN)/(RMAX-RMIN)
# print len(xx)
# xx=xx[0:-1:300]
# yy=yy[0:-1:300]
# print len(xx)
ax.plot( xx, yy,'-.',color='white',linewidth=1.0)
ax.set_title(r'$q=%d,d_f=%s$'%(100*quantile,Df),fontsize='x-small')
#fig.savefig('%s/densityMaps.png'%DIR_OUTPT_figs,bbox_inches='tight',dpi=150)
#---
# mpl.rcParams.update(mpl.rcParamsDefault)
# warnings.filterwarnings('ignore') #--- get rid of warnings
# rc('text', usetex=True)
# font = {'size' : 20}
# matplotlib.rc('font', **font)
plt.show()
In [38]:
# #--- triggering part of nij
# nij_trig=nij[nij['T*']*nij['R*']<=n_thresh]
# df_triggered = swarm_lohi.iloc[nij_trig['Event_id']]
# #--- background part of nij
# nij_background=nij[nij['T*']*nij['R*']>n_thresh]
# nn = len(nij_background)
# nij_background = nij_background.append(nij_removed,verify_integrity=False) #--- append removed part
# assert len(nij_background) == nn + len(nij_removed)
# #--- background events
# background_child = list(set(nij_background['Event_id'])) #--- children
# #
# nij_copy = nij.copy()
# Nij = nij_copy.append(nij_removed)
# background_root = list(set(Nij['Parent_id'])-set(Nij['Event_id'])) #--- root
# #
# background = background_root+background_child #--- total
# assert len(background) == len(set(background)) #--- assert no overlap
# #
# df_background = swarm_lohi.iloc[background]
# assert len(df_triggered) + len(df_background) == len(swarm_lohi), '%s != %s' %(len(df_triggered) + len(df_background),len(swarm_lohi))
# #display(nij_trig.info())
# trig_ratio = 1.0*len(df_triggered) / len(swarm_lohi) #cdf_actual[edges_actual[:-1]<=n_thresh][-1]
# print 'trig_ratio=%s'%trig_ratio
repeat for fake catalog¶
In [39]:
#--- triggering part of nij
nij = Nij_rnd
nij_trig=nij[nij['T*']*nij['R*']<=n_thresh]
df_triggered = swarm_shuffled.iloc[nij_trig['Event_id']]
#--- background part of nij
nij_background=nij[nij['T*']*nij['R*']>n_thresh]
#nn = len(nij_background)
#nij_background = nij_background.append(nij_removed,verify_integrity=False) #--- append removed part
#assert len(nij_background) == nn + len(nij_removed)
#--- background events
background_child = list(set(nij_background['Event_id'])) #--- children
#
nij_copy = nij.copy()
Nij = nij_copy.append(nij_removed)
background_root = list(set(Nij['Parent_id'])-set(Nij['Event_id'])) #--- root
#
background = background_root+background_child #--- total
assert len(background) == len(set(background)) #--- assert no overlap
#
df_background = swarm_shuffled.iloc[background]
assert len(df_triggered) + len(df_background) == len(swarm_shuffled), '%s != %s' %(len(df_triggered) + len(df_background),len(swarm_shuffled))
#display(nij_trig.info())
trig_ratio = 1.0*len(df_triggered) / len(swarm_shuffled) #cdf_actual[edges_actual[:-1]<=n_thresh][-1]
print 'trig_ratio=%s'%trig_ratio
Distributions of $n_{ij}$¶
In [40]:
#--- histogram
nn=np.log10(nij['R*']*nij['T*'])
nmin=nn.min()
nmax=nn.max()
bins=np.linspace(nmin,nmax,int(nmax-nmin)*8)
hist, edge = np.histogram(nn,bins=bins,normed=True)
#--- accumulated histogram
slist=np.array(nn)
slist.sort()
N = len(slist)
d = histogramACCUMLTD( slist.tolist() )
keys=d.keys()
keys.sort()
xx=[];yy=[]
for ikey in keys:
xx.append(d[ikey][0])
yy.append(d[ikey][2])
#------------
#--- plot
#------------
fig= plt.figure(figsize=(4,4))
ax = fig.add_subplot(111)
ax.set_xlabel(r'$log n_{ij}$')
ax.set_ylabel(r'$P(log n_{ij})$')
(nmin,nmax) = (min(slist),max(slist))
ax.set_xlim(floor(nmin),ceil(nmax))
#ax.set_xlim(-7,1)
#ax.set_ylim(0,0.6)
#ax.set_xscale('log')
#ax.set_yscale('log')
ax.plot(edge[:-1],hist,'-o',color='black')
# ax2 = ax.twinx()
# ax2.plot(xx,yy,
# linestyle='-', drawstyle='steps-post',color='red',
# linewidth=1.0) #--- accumulated
# #ax2.set_xlim(-7,1)
# #ax2.set_ylim(0,1200)
# ax2.tick_params(axis='y',colors='red')
# ax2.set_ylabel('$N(<n_{ij})$',color='red')
np.save('actual',np.c_[edge[:-1],hist])
np.save('acc_actual',np.c_[xx,yy])
#fig.savefig('%s/pn_actual.png'%DIR_OUTPT_figs,bbox_inches='tight')
plt.show()
Distributions of random 𝑛𝑖𝑗¶
In [41]:
#--- histogram
nn=np.log10(Nij_rnd['R*']*Nij_rnd['T*'])
nmin=nn.min()
nmax=nn.max()
bins=np.linspace(nmin,nmax,int(nmax-nmin)*8)
hist, edge = np.histogram(nn,bins=bins,normed=True)
#--- accumulated histogram
slist=np.array(nn)
slist.sort()
N = len(slist)
d = histogramACCUMLTD( slist.tolist() )
keys=d.keys()
keys.sort()
xx=[];yy=[]
for ikey in keys:
xx.append(d[ikey][0])
yy.append(d[ikey][2])
#------------
#--- plot
#------------
fig= plt.figure(figsize=(4,4))
ax = fig.add_subplot(111)
ax.set_xlabel(r'$log n_{ij}$')
ax.set_ylabel(r'$P(log n_{ij})$')
(nmin,nmax) = (min(slist),max(slist))
ax.set_xlim(floor(nmin),ceil(nmax))
#ax.set_xlim(-7,1)
#ax.set_ylim(0,0.6)
#ax.set_xscale('log')
#ax.set_yscale('log')
ax.plot(edge[:-1],hist,'-o',color='black')
# ax2 = ax.twinx()
# ax2.plot(xx,yy,
# linestyle='-', drawstyle='steps-post',color='red',
# linewidth=1.0) #--- accumulated
# #ax2.set_xlim(-7,1)
# #ax2.set_ylim(0,1200)
# ax2.tick_params(axis='y',colors='red')
# ax2.set_ylabel('$N(<n_{ij})$',color='red')
np.save('random',np.c_[edge[:-1],hist])
np.save('acc_random',np.c_[xx,yy])
#fig.savefig('%s/pn_shuffled.png'%DIR_OUTPT_figs,bbox_inches='tight')
plt.show()
In [42]:
act = np.load('actual.npy')
rnd = np.load('random.npy')
acc_act = np.load('acc_actual.npy')
acc_rnd = np.load('acc_random.npy')
#------------
#--- plot
#------------
fig= plt.figure(figsize=(4,4))
ax = fig.add_subplot(111)
ax.set_xlabel(r'$log n_{ij}$')
ax.set_ylabel(r'$P(log n_{ij})$')
(nmin,nmax) = (min(slist),max(slist))
ax.set_xlim(floor(nmin),ceil(nmax))
#ax.set_title('HypoDD')
# ax.set_xlim(-7,1)
# ax.set_ylim(0,0.6)
#ax.set_xscale('log')
#ax.set_yscale('log')
ax.plot(act[:,0],act[:,1],'-o',color='black',label='Actual')
ax.plot(rnd[:,0],rnd[:,1],'-s',color='red',label='Shuffled')
ax.plot([np.log10(n_thresh),np.log10(n_thresh)],[0,0.3])
ax.legend(fontsize='xx-small')
# ax2 = ax.twinx()
# ax2.plot(acc_act[:,0],acc_act[:,1],
# linestyle='-', drawstyle='steps-post',color='black',
# linewidth=1.0) #--- accumulated
# ax2.plot(acc_rnd[:,0],acc_rnd[:,1],
# linestyle='-', drawstyle='steps-post',color='red',
# linewidth=1.0) #--- accumulated
# # ax2.set_xlim(-7,1)
# # ax2.set_ylim(0,1200)
# ax2.tick_params(axis='y',colors='red')
# ax2.set_ylabel('$N(<n_{ij})$',color='red')
#fig.savefig('%s/pn_actual_shuffled.png'%DIR_OUTPT_figs,bbox_inches='tight',dpi=75)
plt.show()
plot moment tensor and triggered events¶
In [43]:
from math import *
import numpy as np
import pandas as pd
def arrows(ax,(xc,yc),n1,n3,rr):
[x1,y1]=np.array([xc,yc])+rr*n3[:2]
[xo,yo]=np.array([xc,yc])+.1*rr*n3[:2]
ax.annotate("", (xo,yo), xytext=(x1, y1),
textcoords='data',clip_on=True,
arrowprops=dict(arrowstyle="-|>,head_width=.2,head_length=.4",color="red",linewidth="0.3"))
[x1,y1]=np.array([xc,yc])-rr*n3[:2]
[xo,yo]=np.array([xc,yc])-.1*rr*n3[:2]
ax.annotate("", (xo,yo), xytext=(x1, y1),
textcoords='data', clip_on=True,
arrowprops=dict(arrowstyle="-|>,head_width=.2,head_length=.4",color="red",linewidth="0.3"))
[x1,y1]=np.array([xc,yc])+rr*n1[:2]
[xo,yo]=np.array([xc,yc])+.1*rr*n1[:2]
ax.annotate("", (x1,y1), xytext=(xo, yo),
textcoords='data', clip_on=True,
arrowprops=dict(arrowstyle="-|>,head_width=.2,head_length=.4",color="black",linewidth="0.3"))
[x1,y1]=np.array([xc,yc])-rr*n1[:2]
[xo,yo]=np.array([xc,yc])-.1*rr*n1[:2]
ax.annotate("", (x1,y1), xytext=(xo, yo),
textcoords='data', clip_on=True,
arrowprops=dict(arrowstyle="-|>,head_width=.2,head_length=.4",color="black",linewidth="0.3"))
def getN(phi_az,alpha):
phi_az *= pi/180
alpha *= pi/180
# return np.array([cos(alpha)*cos(phi_az), cos(alpha)*sin(phi_az), sin(alpha) ])
return np.array([cos(alpha)*sin(phi_az), cos(alpha)*cos(phi_az), sin(alpha) ]) #--- azimuth with respect to north
def tensProd(n1,n2):
n=3
return np.array([[n1[i]*n2[j] for j in xrange(3)] for i in xrange(3)])
def arrows(ax,(xc,yc),n1,n3,rr):
[x1,y1]=np.array([xc,yc])+rr*n3[:2]
[xo,yo]=np.array([xc,yc])+.1*rr*n3[:2]
ax.annotate("", (xo,yo), xytext=(x1, y1),
textcoords='data',clip_on=True,
arrowprops=dict(arrowstyle="-|>,head_width=.2,head_length=.4",color="red",linewidth="0.3"))
[x1,y1]=np.array([xc,yc])-rr*n3[:2]
[xo,yo]=np.array([xc,yc])-.1*rr*n3[:2]
ax.annotate("", (xo,yo), xytext=(x1, y1),
textcoords='data', clip_on=True,
arrowprops=dict(arrowstyle="-|>,head_width=.2,head_length=.4",color="red",linewidth="0.3"))
[x1,y1]=np.array([xc,yc])+rr*n1[:2]
[xo,yo]=np.array([xc,yc])+.1*rr*n1[:2]
ax.annotate("", (x1,y1), xytext=(xo, yo),
textcoords='data', clip_on=True,
arrowprops=dict(arrowstyle="-|>,head_width=.2,head_length=.4",color="black",linewidth="0.3"))
[x1,y1]=np.array([xc,yc])-rr*n1[:2]
[xo,yo]=np.array([xc,yc])-.1*rr*n1[:2]
ax.annotate("", (x1,y1), xytext=(xo, yo),
textcoords='data', clip_on=True,
arrowprops=dict(arrowstyle="-|>,head_width=.2,head_length=.4",color="black",linewidth="0.3"))
def PlotMomentTensor(trigger_list, swarm_lohi, nij_trig, nmin=30 ):
for triggerID, xx in zip(trigger_list,xrange(10000)):
try:
#--- list of children
index_trigger = swarm_lohi[swarm_lohi['Event ID']==triggerID].index[0]
children_index_list = nij_trig[nij_trig['Parent_id']==index_trigger]['Event_id']
if len(children_index_list) < nmin:
continue
#--- plot moment tensor
# #--- parse moment tensor
# df_trigger = df_moment[df_moment['Event ID'] == triggerID]
df_trigger = swarm_lohi[swarm_lohi['Event ID'] == triggerID]
n1 = getN(df_trigger['Azimuth(T)'],df_trigger['Plunge(T)']) #--- principal directions (azimuth, plunge)
n3 = getN(df_trigger['Azimuth(P)'],df_trigger['Plunge(P)'])
n2 = np.cross(n3,n1) #getN(df_trigger['Azimuth(N)'],df_trigger['Plunge(N)'])
if np.isnan(n1[0]):
continue
#--- project t, p
n1 -= n1[2] * np.array([0.0,0.0,1.0])
n3 -= n3[2] * np.array([0.0,0.0,1.0])
#--- plot events
fig = plt.figure(figsize=(4,4))
ax = fig.add_subplot(111)
x = swarm_lohi.iloc[children_index_list]['longitude']
y = swarm_lohi.iloc[children_index_list]['latitude']
mag = swarm_lohi.iloc[children_index_list]['magnitude']
xc = swarm_lohi.iloc[index_trigger]['longitude']
yc = swarm_lohi.iloc[index_trigger]['latitude']
mag_c = swarm_lohi.iloc[index_trigger]['magnitude']
ax.scatter(x,y,s=np.exp(mag),alpha=0.2)
ax.scatter(xc,yc,s=np.exp(mag_c),marker='*',facecolors='yellow',color='black')
ax.set_title(r'$m=%2.1f$'%mag_c,fontsize='small')
#--- draw planes
dd=max(x.max()-x.min(),y.max()-y.min())
arrows(ax,(xc,yc),n1, n3, dd/3)
ax.set_xlim(xc-dd/2,xc+dd/2)
ax.set_ylim(yc-dd/2,yc+dd/2)
# fig.savefig('%s/spatialMap%s.png'%(DIR_OUTPT_figs,triggerID),bbox_inches='tight',dpi=150)
except:
continue
# print (xc,yc),(x1, y1)
plt.show()
#trigger_list = set(swarm_lohi.iloc[nij_trig['Parent_id']]['Event ID'])
trigger_list = set(swarm_shuffled.iloc[nij_trig['Parent_id']]['Event ID'])
#PlotMomentTensor(trigger_list, swarm_lohi, nij_trig, nmin=30 )
PlotMomentTensor(trigger_list, swarm_shuffled, nij_trig, nmin=10 )
transform the frame¶
In [44]:
# #trigger_list = set(swarm_lohi.iloc[nij_trig['Parent_id']]['Event ID']) & set(df_moment['Event ID'])
# fig = plt.figure(figsize=(4,4))
# ax = fig.add_subplot(111)
# for triggerID in trigger_list:
# #--- parse moment tensor
# # df_trigger = df_moment[df_moment['Event ID'] == triggerID]
# df_trigger = swarm_lohi[swarm_lohi['Event ID'] == triggerID]
# n1 = getN(df_trigger['Azimuth(T)'],df_trigger['Plunge(T)']) #--- principal directions (azimuth, plunge)
# n3 = getN(df_trigger['Azimuth(P)'],df_trigger['Plunge(P)'])
# n2 = np.cross(n3,n1) #getN(df_trigger['Azimuth(N)'],df_trigger['Plunge(N)'])
# if np.isnan(n1[0]):
# continue
# Q=np.c_[n1,n3,n2].T #--- transformation
# #--- list of children
# index_trigger = swarm_lohi[swarm_lohi['Event ID']==triggerID].index[0]
# children_index_list = nij_trig[nij_trig['Parent_id']==index_trigger]['Event_id']
# #--- plot events
# x = swarm_lohi.iloc[children_index_list]['x(km)']
# y = swarm_lohi.iloc[children_index_list]['y(km)']
# z = swarm_lohi.iloc[children_index_list]['z(km)']
# xc = swarm_lohi.iloc[index_trigger]['x(km)']
# yc = swarm_lohi.iloc[index_trigger]['y(km)']
# zc = swarm_lohi.iloc[index_trigger]['z(km)']
# mag = swarm_lohi.iloc[children_index_list]['magnitude']
# mag_c = swarm_lohi.iloc[index_trigger]['magnitude']
# r_local = np.matmul(Q,np.c_[x-xc,y-yc,z-zc].T).T #Transform
# ax.scatter(r_local[:,0],r_local[:,1],c='C0',alpha=0.1,s=np.exp(mag))
# # ax.scatter(xc,yc,color='yellow')
# #--- plot moment tensor
# #--- project t, p
# n1 = np.array([1.0,0.0])
# n3 = np.array([0.0,1.0])
# rr=4 #.2*(r_local[:,0].max()-r_local[:,0].min())
# #--- draw axis
# xc = 0.0
# yc = 0.0
# zc = 0.0
# [x1,y1]=np.array([xc,yc])+rr*n3[:2]
# ax.annotate("", (xc,yc), xytext=(x1, y1),
# textcoords='data',clip_on=True,
# arrowprops=dict(arrowstyle="-|>,head_width=.2,head_length=.4",color="red",linewidth="0.3"))
# [x1,y1]=np.array([xc,yc])-rr*n3[:2]
# ax.annotate("", (xc,yc), xytext=(x1, y1),
# textcoords='data',clip_on=True,
# arrowprops=dict(arrowstyle="-|>,head_width=.2,head_length=.4",color="red",linewidth="0.3"))
# [x1,y1]=np.array([xc,yc])+rr*n1[:2]
# ax.annotate("", (x1,y1), xytext=(xc, yc),
# textcoords='data',clip_on=True,
# arrowprops=dict(arrowstyle="-|>,head_width=.2,head_length=.4",color="black",linewidth="0.3"))
# [x1,y1]=np.array([xc,yc])-rr*n1[:2]
# ax.annotate("", (x1,y1), xytext=(xc, yc),
# textcoords='data',clip_on=True,
# arrowprops=dict(arrowstyle="-|>,head_width=.2,head_length=.4",color="black",linewidth="0.3"))
# dd=20 #max(r_local[:,0].max()-r_local[:,0].min(),r_local[:,1].max()-r_local[:,1].min())
# ax.set_xlim(xc-dd/2,xc+dd/2)
# ax.set_ylim(yc-dd/2,yc+dd/2)
# ax.set_xlabel(r'$x(km)$')
# ax.set_ylabel(r'$y(km)$')
# #fig.savefig('%s/spatialMap.png'%(DIR_OUTPT_figs),bbox_inches='tight',dpi=150)
# plt.show()
magnitude bins¶
In [45]:
def MagBins( trigger_list, swarm_lohi, nij_trig, m):
r_local_m_bins = {}
mag_m_bins = {}
for triggerID in trigger_list:
#--- parse moment tensor
# df_trigger = df_moment[df_moment['Event ID'] == triggerID]
df_trigger = swarm_lohi[swarm_lohi['Event ID'] == triggerID]
n1 = getN(df_trigger['Azimuth(T)'],df_trigger['Plunge(T)']) #--- principal directions (azimuth, plunge)
n3 = getN(df_trigger['Azimuth(P)'],df_trigger['Plunge(P)'])
n2 = np.cross(n3,n1) #getN(df_trigger['Azimuth(N)'],df_trigger['Plunge(N)'])
if np.isnan(n1[0]):
continue
magnitude_indx = m.searchsorted(df_trigger['magnitude'].iloc[0])
Q=np.c_[n1,n3,n2].T #--- transformation
#--- list of children
index_trigger = swarm_lohi[swarm_lohi['Event ID']==triggerID].index[0]
children_index_list = nij_trig[nij_trig['Parent_id']==index_trigger]['Event_id']
#--- plot events
x = swarm_lohi.iloc[children_index_list]['x(km)']
y = swarm_lohi.iloc[children_index_list]['y(km)']
z = swarm_lohi.iloc[children_index_list]['z(km)']
xc = swarm_lohi.iloc[index_trigger]['x(km)']
yc = swarm_lohi.iloc[index_trigger]['y(km)']
zc = swarm_lohi.iloc[index_trigger]['z(km)']
mag = swarm_lohi.iloc[children_index_list]['magnitude']
mag_c = swarm_lohi.iloc[index_trigger]['magnitude']
r_local = np.matmul(Q,np.c_[x-xc,y-yc,z-zc].T).T #Transform
if magnitude_indx in r_local_m_bins:
# print r_local_m_bins[ magnitude_indx ].shape, r_local.shape
r_local_m_bins[ magnitude_indx ] = np.concatenate((r_local_m_bins[ magnitude_indx] ,r_local),axis=0)
mag_m_bins[ magnitude_indx ] = np.concatenate((mag_m_bins[ magnitude_indx] ,mag),axis=0)
else:
r_local_m_bins[ magnitude_indx ] = r_local[:,:]
mag_m_bins[ magnitude_indx ] = mag.copy()
xc = yc = 0.0
for magnitude_indx in r_local_m_bins:
fig = plt.figure(figsize=(4,4))
ax = fig.add_subplot(111)
r_local = r_local_m_bins[ magnitude_indx ]
mag = mag_m_bins[ magnitude_indx ]
# print r_local.shape
ax.scatter(r_local[:,0],r_local[:,1],c='C0',alpha=0.1,s=np.exp(mag))
ax.set_title(r'$m=%2.1f$'%m[magnitude_indx],fontsize='small')
dd = 2*max(np.std(r_local[:,0]),np.std(r_local[:,1])) #np.abs(r_local[:,0]).max(),np.abs(r_local[:,1]).max())/4
ax.set_xlim(xc-dd,xc+dd)
ax.set_ylim(yc-dd,yc+dd)
ax.set_xlabel(r'$x(km)$')
ax.set_ylabel(r'$y(km)$')
arrows(ax,(xc,yc),np.array([1.0,0.0]),np.array([0.0,1.0]),dd/3)
# fig.savefig('map%s.png'%magnitude_indx,dpi=75,bbox_inches='tight')
plt.show()
return r_local_m_bins
m=np.array([1.999999,
2.99999925,
3.9999995000000004,
4.99999975,
6.0,
6.41,
7.09,
7.109999999999999])
#r_local_m_bins = MagBins( trigger_list, swarm_lohi, nij_trig, m)
r_local_m_bins = MagBins( trigger_list, swarm_shuffled, nij_trig, m)
interpolation¶
In [46]:
from scipy import stats
def interpolation(r_local_m_bins):
xc = yc = 0.0
for magnitude_indx in r_local_m_bins:
try:
#--- interpolate
r_local = r_local_m_bins[ magnitude_indx ]
dd = 2*max(np.std(r_local[:,0]),np.std(r_local[:,1])) #np.abs(r_local[:,0]).max(),np.abs(r_local[:,1]).max())/4
ymin = xmin = -dd
ymax = xmax = +dd
X, Y = np.mgrid[ xmin:xmax:200j, ymin:ymax:200j]
positions = np.vstack([X.ravel(), Y.ravel()])
values = np.vstack([r_local[:,0], r_local[:,1]])
kernel = stats.gaussian_kde(values)
kernel.set_bandwidth(bw_method=kernel.factor / 10.) #--- smoothing length
Z = np.reshape(kernel(positions).T, X.shape)
#--- plot
fig = plt.figure(figsize=(4,4))
ax = fig.add_subplot(111)
ax.imshow(np.rot90(Z), cmap='coolwarm', #plt.cm.gist_earth_r,
extent=[xmin, xmax, ymin, ymax])
ax.plot(r_local[:,0], r_local[:,1], 'k.', markersize=1)
ax.set_xlim(xc-dd/2,xc+dd/2)
ax.set_ylim(yc-dd/2,yc+dd/2)
ax.set_xlabel(r'$x(km)$',fontsize='small')
ax.set_ylabel(r'$y(km)$',fontsize='small')
ax.set_title(r'$m=%2.1f$'%m[magnitude_indx],fontsize='small')
arrows(ax,(xc,yc),np.array([1.0,0.0]),np.array([0.0,1.0]),dd/6)
except:
continue
plt.show()
interpolation(r_local_m_bins)
Correlations¶
In [47]:
def Correlations(r_local_m_bins):
xc = yc = 0.0
for magnitude_indx in r_local_m_bins:
try:
#--- interpolate
r_local = r_local_m_bins[ magnitude_indx ]
dd = max(np.std(r_local[:,0]),np.std(r_local[:,1])) #np.abs(r_local[:,0]).max(),np.abs(r_local[:,1]).max())/4
ymin = xmin = -dd
ymax = xmax = +dd
X, Y = np.mgrid[ xmin:xmax:201j, ymin:ymax:201j]
positions = np.vstack([X.ravel(), Y.ravel()])
values = np.vstack([r_local[:,0], r_local[:,1]])
kernel = stats.gaussian_kde(values)
kernel.set_bandwidth(bw_method=kernel.factor / 10.) #--- smoothing length
Z = np.reshape(kernel(positions).T, X.shape)
#--- fft
Z -= Z.mean()
Z /= Z.std()
Z=np.rot90(Z)
Zq = np.abs(np.fft.fft2(Z))**2
zfield = np.fft.ifft2(Zq).real
zfield = np.fft.ifftshift(zfield) / (zfield.shape[0]*zfield.shape[1])
#--- plot
fig = plt.figure(figsize=(4,4))
ax = fig.add_subplot(111)
pos = ax.imshow(zfield,cmap='bwr',extent=[xmin, xmax, ymin, ymax]) #,vmin=-0.5, vmax=.5)
ax.contour( zfield, np.arange(zfield.min(),zfield.max(),0.15) ,
extent=[xmin, xmax, ymin, ymax],
origin='image',colors='black',linewidths=0.2)
# fig.colorbar( pos, fraction = 0.04) #, format = '%2.1f' )
ax.set_xlim(xc-dd/2,xc+dd/2)
ax.set_ylim(yc-dd/2,yc+dd/2)
# ax.set_xlabel(r'$x(km)$')
# ax.set_ylabel(r'$y(km)$')
ax.set_title(r'$m=%2.1f, n_{th}=%2.1e$'%(m[magnitude_indx],n_thresh),fontsize='small')
arrows(ax,(xc,yc),np.array([1.0,0.0]),np.array([0.0,1.0]),dd/3)
fig.savefig('corr_map%s.png'%magnitude_indx,dpi=.55*75,bbox_inches='tight')
except:
continue
plt.show()
Correlations(r_local_m_bins)
quantify anisotropy¶
In [48]:
xc = yc = 0.0
for magnitude_indx in [7]: #r_local_m_bins:
#--- interpolate
r_local = r_local_m_bins[ magnitude_indx ]
dd = max(np.abs(r_local[:,0]).max(),np.abs(r_local[:,1]).max())
ymin = xmin = -dd
ymax = xmax = +dd
X, Y = np.mgrid[ xmin:xmax:401j, ymin:ymax:401j]
positions = np.vstack([X.ravel(), Y.ravel()])
values = np.vstack([r_local[:,0], r_local[:,1]])
kernel = stats.gaussian_kde(values)
kernel.set_bandwidth(bw_method=kernel.factor / 10.) #--- smoothing length
Z = np.reshape(kernel(positions).T, X.shape)
#--- fft
Z -= Z.mean()
Z /= Z.std()
Z=np.rot90(Z)
Zq = np.abs(np.fft.fft2(Z))**2
zfield = np.fft.ifft2(Zq).real
zfield = np.fft.ifftshift(zfield) / (zfield.shape[0]*zfield.shape[1])
#--- plot
fig = plt.figure(figsize=(4,4))
ax = fig.add_subplot(111)
pos = ax.imshow(zfield,cmap='bwr',extent=[xmin, xmax, ymin, ymax]) #,vmin=-0.5, vmax=.5)
ax.contour( zfield, np.arange(zfield.min(),zfield.max(),0.15) ,
extent=[xmin, xmax, ymin, ymax],
origin='image',colors='black',linewidths=0.2)
fig.colorbar( pos, fraction = 0.04) #, format = '%2.1f' )
dd = max(np.std(r_local[:,0]),np.std(r_local[:,1]))*2
ax.set_xlim(xc-dd/2,xc+dd/2)
ax.set_ylim(yc-dd/2,yc+dd/2)
ax.set_xlabel(r'$x(km)$')
ax.set_ylabel(r'$y(km)$')
ax.set_title(r'$m=%2.1f$'%m[magnitude_indx],fontsize='small')
arrows(ax,(xc,yc),np.array([1.0,0.0]),np.array([0.0,1.0]),dd/3)
# fig.savefig('corr_map%s.png'%magnitude_indx,dpi=75,bbox_inches='tight')
plt.show()
In [49]:
R=[1,2,4]
fig = plt.figure(figsize=(4,4))
ax = fig.add_subplot(111)
ax.set_xlabel(r'$\theta$')
ax.set_ylabel(r'$c(\theta)$')
rsq = X*X+Y*Y
for r in R:
dr=0.1*r
indices=np.all([rsq<(r+dr)**2, rsq>(r-dr)**2], axis=0)
xx=Y[indices]
yy=-X[indices]
theta=180*np.arctan2(yy,xx)/pi
rho = zfield[indices]
rho = rho[theta>=0.0]
rho /= (np.abs(rho)).max()
theta = theta[theta>=0.0]
ax.scatter(theta,rho,label=r'$r=%3.2f$'%r,s=12)
ax.legend(fontsize='x-small')
plt.show()
In [50]:
THETA=[45.0, 90.0, 135.0]
fig = plt.figure(figsize=(4,4))
ax = fig.add_subplot(111)
ax.set_xlabel(r'$r$')
ax.set_ylabel(r'$c(r)$')
ax.set_xscale('log')
ax.set_yscale('log')
ax.set_ylim(1e-2,1)
for theta in THETA:
dt=0.01*theta
xx=Y
yy=-X
indices=np.abs(np.angle(xx+1j*yy,deg=True)-theta) < dt
xx=xx[indices]
yy=yy[indices]
rr=np.sqrt(xx*xx+yy*yy)
rho = zfield[indices]
ax.plot(rr,rho,label=r'$\theta=%3.1f$'%theta)
ax.legend(fontsize='x-small')
plt.show()
plot moment tensor and triggered events¶
In [51]:
#--- density plots: rho(r)
#--- split based on the mainshock's magnitude
import numpy as np
import math
def AddTime( df_trig, df_complete ):
prefact = 1.0 / ( 24.0 * 60 * 60 ) #--- daily
x=df_complete.loc[ df_trig['Event_id'] ]
y=df_complete.loc[ df_trig['Parent_id'] ]
x.reset_index(inplace=True)
y.reset_index(inplace=True)
df_trig['T'] = x['date']-y['date']
df_trig['T'] = df_trig['T'].apply(lambda x: x.total_seconds() * prefact)
def RemovePair( df, cs ):
return df [ df[ 'R' ] <= df[ 'T' ] * cs ]
Mlist=m=[1.999999,
2.99999925,
3.9999995000000004,
4.99999975,
6.0,
6.41,
7.09,
7.109999999999999]
#--- choose m0<m<m1
X={}
rho_dict={}
m_range={}
Err={}
m_mean={}
for i in xrange( len(m) - 1 ):
try:
m0 = m[ i ]
m1 = m[ i + 1 ]
df_trig, m_mean[ i ],junk = GetPairsWithSpecifiedParentMag((m0,m1),swarm_lohi,nij_trig) #--- get parent with m0<m<m1
df_trig.reset_index( inplace = True, drop = True )
#--- rho plots
n_decades = int( math.ceil( log(df_trig['R'].max()/df_trig['R'].min(),10) ) )
nbin_per_decade = 4
nbins = nbin_per_decade * n_decades
bins = np.logspace(log(df_trig['R'].min(),10)-1.e-10,
log(df_trig['R'].max(),10)+1.e-10,nbins)
bins = AdjustBins(df_trig['R'],bins)
rho, xedges=np.histogram(df_trig['R'],
density=True,
bins=bins)
hist, xedges=np.histogram(df_trig['R'],
bins=bins)
x_bins, junk=np.histogram(df_trig['R'], #--- histogram
bins=bins,
weights = df_trig['R'])
#--- rm empty bins
x_bins = x_bins[ hist != 0 ]
rho = rho[ hist != 0 ]
hist = hist[ hist != 0 ]
#--- poisson err
err = rho/np.sqrt(hist)
x_bins /= hist
#--- scattered plot
fig=plt.figure(figsize=(8,4))
ax=fig.add_subplot(1,2,1)
ax.set_title('$%2.1f<m<%2.1f$'%(m0,m1))
ax.set_xscale('log')
ax.set_yscale('log')
ax.set_xlabel('$t$')
ax.set_ylabel('$r$')
ax.set_xlim(1e-5,10)
ax.set_ylim(1e-4,1e2)
ax.scatter(df_trig['T'],df_trig['R'],alpha=0.1)
#--- discretization effects
# dt_min=df_trig['T'].min()
# dt_max=df_trig['T'].max()
# dr_min=df_trig['R'].min()
# dr_max=df_trig['R'].max()
# ax.plot([dt_min,dt_min],[dr_min,dr_max],
# '-',color='blue')
# ax.plot([dt_max,dt_max],[dr_min,dr_max],
# '-',color='blue')
# ax.plot([dt_min,dt_max],[dr_min,dr_min],
# '-',color='blue')
# ax.plot([dt_min,dt_max],[dr_max,dr_max],
# '-',color='blue')
# ax.set_ylim(dr_min/2,dr_max*2)
# ax.plot([dt_min,dt_max],[dt_min*cs,dt_max*cs],
# '-',color='red')
#--- rho
ax=fig.add_subplot(1,2,2)
ax.set_xlim(1e-4,1e2)
ax.set_ylim(1e-5,1e1)
ax.set_xscale('log')
ax.set_yscale('log')
ax.set_xlabel('$r$')
ax.set_ylabel('$P(r)$')
ax.errorbar(x_bins,rho, yerr=err)
X[i] = x_bins[:]
rho_dict[i]=rho[:]
m_range[i]=np.array([m0,m1])
Err[i]=err[:]
# plt.savefig('%s/rho_r.%s.png'%(DIR_OUTPT_figs,i),dpi=50,bbox_inches='tight')
except:
continue
plt.show()
Declustered Catalog¶
In [52]:
df_triggered.head()
Out[52]:
In [53]:
#--- plot complete catalog
def ConvertDailyRate(hist, bin_edges ):
#---convert data to daily rate
t0 = pd.to_datetime( bin_edges[ 0 ] )
t1 = pd.to_datetime( bin_edges[ 1 ] )
delta_t = ( t1 - t0 ).total_seconds() / ( 60 * 60 * 24)
hist *= ( bin_edges[ 1 ] - bin_edges[ 0 ] ) / delta_t
def ActivityRate( df ):
nbins = int( (df['date'].max()-df['date'].min()).days / 2 ) #--- number of bins
tmax = df['date'].max().value #--- min/max
tmin = df['date'].min().value
hist, bin_edges = np.histogram(df['date'].apply(lambda x:x.value),
bins=np.linspace(tmin,tmax,nbins+1,endpoint=True),density=True) #--- probability dist.
hist *= len( df['date'] ) #--- int(hist).dt=n
cumm_number = np.cumsum(hist)*(bin_edges[1]-bin_edges[0]) #--- accumulated number
ConvertDailyRate( hist, bin_edges ) #--- daily activity
return bin_edges, hist, cumm_number
class Tlohi:
def __init__(self,lo,hi):
self.lo = lo
self.hi = hi
#---------------------------------------------------------------------------------
#-----------------
#-----------------
#-----------------
#---------------------------------------------------------------------------------
#--- set min/max time to avoid temporal incompletenesss issue
df_lohi = DataFrameSubSet( swarm, #--- complete catalog
'magnitude',
( mc, sys.maxint ) )
df_lohi = GetCartesian( df_lohi )
df_lohi.reset_index(inplace=True,drop=True)
#--- activity rate
bin_edges, hist, cumm_number = ActivityRate( df_lohi )
#--- temporal map
fig = plt.figure(figsize=(8,9))#,dpi=150)
ax1=fig.add_subplot(311)
ax2=fig.add_subplot(312)
ax3=fig.add_subplot(313)
ax1.set_ylabel('$M$')
ax1.set_xlim(df_lohi['date'].min(),df_lohi['date'].max())
ax1.tick_params(axis='both',labelsize=18)
ax2.set_ylabel('$M$')
ax2.set_xlim(df_lohi['date'].min(),df_lohi['date'].max())
ax2.tick_params(axis='both',labelsize=18)
ax3.set_ylabel('$M$')
ax3.set_xlim(df_lohi['date'].min(),df_lohi['date'].max())
ax3.tick_params(axis='both',labelsize=18)
#ax1.set_ylim(mc,2.5)
#ax1.set_xlim(pd.to_datetime('2019-03-01'),pd.to_datetime('2019-03-30'))
#
# ax1R = ax1.twinx() # instantiate a second axes that shares the same x-axis
# ax1R.set_ylabel('daily activity rate',color='red')
# ax1R.set_yscale('log')
# ax1R.tick_params(axis='y',labelsize=18,colors='red')
#
#ax2 = fig.add_subplot(212)
#ax2.set_ylim(mc,2.5)
#ax2.set_ylabel('Max Rate (m3/min)')
#ax2.set_ylim(11.9,12.1)
#ax2.set_xlim(pd.to_datetime('2019-03-01'),pd.to_datetime('2019-03-30'))
#
#--- plot
ax1.scatter(df_triggered['date'],df_triggered['magnitude'],
s=2**(df_triggered['magnitude']),
alpha=0.05,color='blue', label = 'Triggered')
#
ax2.scatter(df_background['date'],df_background['magnitude'],
s=2**(df_background['magnitude']),
alpha=0.05,color='red', label = 'Declustered')
#
ax3.scatter(df_lohi['date'],df_lohi['magnitude'],
s=2**(df_lohi['magnitude']),
alpha=0.05,color='black', label = 'Total')
fig.legend(loc='best',frameon=True,labelspacing=0)
#ax1R.plot(pd.to_datetime(bin_edges[:-1]),hist,'r-',linewidth=1)
#DrawFrame(ax1, (0.11,0.07),(0.32,0.1),0.01)
ax3.xaxis.set_major_formatter(dates.DateFormatter('%b %y'))
fig.autofmt_xdate()
#fig.savefig('%s/timeSeries_ok.png'%DIR_OUTPT_figs,dpi=150,bbox_inches='tight')
plt.show()
In [54]:
#--- plot spatial map
#--- fault map california: temporal evolution of events
#--- set min/max time to avoid temporal incompletenesss issue
df_lohi = DataFrameSubSet( swarm, #--- complete catalog
'magnitude',
( mc, sys.maxint ) )
df_lohi = GetCartesian( df_lohi )
df_lohi.reset_index(inplace=True,drop=True)
# df_triggered = GetCartesian( df_triggered )
# df_background = GetCartesian( df_background )
xlo = df_lohi['x(km)'].min()
xhi = df_lohi['x(km)'].max()
ylo = df_lohi['y(km)'].min()
yhi = df_lohi['y(km)'].max()
L = max(xhi-xlo,yhi-ylo)
exp = 2
df_triggered.plot.scatter('x(km)','y(km)',
s=exp**(df_triggered['magnitude']),
color = 'blue', label = 'triggered',xlim=(0,L),ylim=(0,L),
# c='date',cmap='jet',
alpha=0.01,
figsize=(4,4)) #--- plot
df_background.plot.scatter('x(km)','y(km)',
s=exp**(df_background['magnitude']),
color = 'red', label = 'background',xlim=(0,L),ylim=(0,L),
# c='date',cmap='jet',
alpha=0.01,
figsize=(4,4)) #--- plot
df_lohi.plot.scatter('x(km)','y(km)',
s=exp**(df_lohi['magnitude']),
color = 'black', label = 'Total',xlim=(0,L),ylim=(0,L),
# c='date',cmap='jet',
alpha=0.01,
figsize=(4,4)) #--- plot
plt.show()
#plt.savefig('%s/map.png'%DIR_OUTPT_figs,dpi=150,bbox_inches='tight')
In [55]:
#trig_ratio *= 0.75
#n_thresh_new = edges_actual[:-1][cdf_actual <= trig_ratio][-1]
#new_quantile = cdf[edges[:-1]<=n_thresh_new][-1]
#print 'new_quantile=%s'%new_quantile
#n_thresh = n_thresh_new
In [56]:
#--- plot clusters
def Inside(t,(tmin,tmax)):
if tmin<= t<tmax:
return True
return False
def GetTrigList( nij_trig ):
d_trig = {}
for items in nij_trig.itertuples():
triggerID = items.Parent_id
d_trig.setdefault( triggerID, [] ).append( items.Event_id )
return d_trig
def PlotArrowsTime(df_complete,d_trig, (tmin,tmax), (xmin,xmax), (ymin,ymax) ):
tlist=[]
mlist=[]
for triggerID in d_trig: #--- mother events
t0 = df_complete['date'].iloc[ triggerID ] #--- time of mother event
m0 = df_complete['magnitude'].iloc[triggerID] #--- magnitude
if not ( Inside(t0,(tmin,tmax) ) and #--- within the given interval
Inside(swarm_lohi['x(km)'].iloc[triggerID],(xmin,xmax)) and
Inside(swarm_lohi['y(km)'].iloc[triggerID],(ymin,ymax)) ):
continue
# x0 = md.date2num( t0 ) #--- convert to time object
# y0 = m0 #--- magnitude
tlist.append( t0 )
mlist.append( m0 )
for daughter_id in d_trig[triggerID]: #--- children
t1 = df_complete['date'].iloc[ daughter_id ] #--- time
m1 = df_complete['magnitude'].iloc[ daughter_id ] #--- magnitude
tlist.append( t1 )
mlist.append( m1 )
if not ( Inside(t1,(tmin,tmax) ) and #--- within the given interval
Inside(swarm_lohi['x(km)'].iloc[daughter_id],(xmin,xmax)) and
Inside(swarm_lohi['y(km)'].iloc[daughter_id],(ymin,ymax)) ):
continue
# x1 = md.date2num( t1 ) #--- convert to time object
# y1 = m1 #--- magnitude
# xw = x1 - x0 #--- t_child-t_parent
# yw = y1 - y0 #--- m_child - m_parent
plt.annotate("", (t1,m1), xytext=(t0, m0),
textcoords='data',
arrowprops=dict(arrowstyle="-|>,head_width=.4,head_length=.8",color="b",linewidth="0.3"))
#--- plot circles
df=pd.DataFrame({'date':tlist,'mag':mlist})
plt.scatter(df['date'], df['mag'],
s=4**(df['mag']),
alpha=1,
facecolors='red',color='black')
#plt.savefig('timeSeries.png')
#--------------------------------------
#----- key: event value: aftershock id
#--------------------------------------
d_trig = GetTrigList( nij_trig )
#--------------------
#----- subset (the same as trig. analysis)
#--------------------
swarm_lohi = DataFrameSubSet( swarm, #--- complete catalog
'magnitude',
( mc, sys.maxint ) )
swarm_lohi.reset_index(inplace=True,drop=True)
#--------------------
#--- cartesian coords
#--------------------
swarm_lohi = GetCartesian( swarm_lohi )
# #--- plot arrows
# #dt=30
# for ii in xrange(1):
# #--- setup
# fig = plt.figure(figsize=(16,4),frameon=False) #, dpi=300)
# #--- xlimit
# xmin = swarm_lohi['longitude'].min()
# xmax = swarm_lohi['longitude'].max()
# ymin = swarm_lohi['latitude'].min()
# ymax = swarm_lohi['latitude'].max()
# plt.tick_params(axis='x', labelsize=14)
# plt.tick_params(axis='y', labelsize=14)
# #--- plot all events
# plt.ylim(mc,swarm_lohi['magnitude'].max())
# plt.scatter(swarm_lohi['date'],swarm_lohi['magnitude'],
# s=2*np.exp(swarm_lohi['magnitude']),
# alpha=0.1)
# key_max = swarm_lohi.loc[nij_trig.groupby(by='Parent_id').groups.keys()]['magnitude'].sort_values(ascending=False).index[ii]
# # print 'key=',key_max
# # print 't=',swarm_lohi.loc[key_max]['date']
# # print 'x=',swarm_lohi.loc[key_max]['x(km)'],
# # print 'y=',swarm_lohi.loc[key_max]['y(km)'],
# # print 'z=',swarm_lohi.loc[key_max]['z(km)']
# dt = nij_trig[nij_trig['Parent_id']==key_max]['T'].max()
# dx = nij_trig[nij_trig['Parent_id']==key_max]['R'].max()
# tt=swarm_lohi['date'].loc[key_max]
# xx = swarm_lohi.loc[key_max][['x(km)','y(km)','z(km)']]
# PlotArrowsTime( swarm_lohi, d_trig,
# ( tt+datetime.timedelta(days=-dt),tt+datetime.timedelta(days=+dt)),
# (xx['x(km)']-dx,xx['x(km)']+dx),
# (xx['y(km)']-dx,xx['y(km)']+dx) )
# plt.xlim(tt+datetime.timedelta(days=-dt),tt+datetime.timedelta(days=+dt))
In [57]:
# #--- plot clusters
# def Inside(t,(tmin,tmax)):
# if tmin<= t<tmax:
# return True
# return False
# def GetTrigList( nij_trig ):
# d_trig = {}
# for items in nij_trig.itertuples():
# triggerID = items.Parent_id
# d_trig.setdefault( triggerID, [] ).append( items.Event_id )
# return d_trig
# def PlotArrowsSpace(df_complete,d_trig, (tmin,tmax), (xmin,xmax), (ymin,ymax) ):
# xlist=[]
# ylist=[]
# mlist=[]
# for triggerID in d_trig: #--- mother events
# t0 = df_complete['date'].iloc[ triggerID ] #--- time of mother event
# ( x0, y0 ) = ( swarm_lohi['longitude'].iloc[triggerID],
# swarm_lohi['latitude'].iloc[triggerID] )
# m0 = df_complete['magnitude'].iloc[triggerID] #--- magnitude
# # if not ( Inside(t0,(tmin,tmax) ) and #--- within the given interval
# # Inside(x0,(xmin,xmax)) and
# # Inside(y0,(ymin,ymax)) ):
# # continue
# for daughter_id in d_trig[triggerID]: #--- children
# t1 = df_complete['date'].iloc[ daughter_id ] #--- time
# ( x1, y1 ) = ( swarm_lohi['longitude'].iloc[ daughter_id ],
# swarm_lohi['latitude'].iloc[ daughter_id ] )
# m1 = df_complete['magnitude'].iloc[ daughter_id ] #--- magnitude
# xlist.append( x1 )
# ylist.append( y1 )
# mlist.append( m1 )
# # if not ( Inside(t1,(tmin,tmax) ) and #--- within the given interval
# # Inside(x1,(xmin,xmax)) and
# # Inside(y1,(ymin,ymax)) ):
# # continue
# ax.annotate("", (x1,y1), xytext=(x0, y0),
# textcoords='data',
# arrowprops=dict(arrowstyle="-|>,head_width=.2,head_length=.8",color="b",linewidth="0.3"))
# #--- plot mother
# plt.scatter(x0,y0,
# s=exponent**m0,
# marker='*',
# facecolors='yellow',color='black',
# alpha=1.0)
# #--- plot circles
# df=pd.DataFrame({'x(km)':xlist,'y(km)':ylist,'m':mlist})
# ax.scatter(df['x(km)'], df['y(km)'],
# s=exponent**(df['m']),
# alpha=1,
# facecolors='red',color='black')
# #--------------------------------------
# #----- key: event value: aftershock id
# #--------------------------------------
# d_trig = GetTrigList( nij_trig )
# #--------------------
# #----- subset (the same as trig. analysis)
# #--------------------
# swarm_lohi = DataFrameSubSet( swarm, #--- complete catalog
# 'magnitude',
# ( mc, sys.maxint ) )
# swarm_lohi.reset_index(inplace=True,drop=True)
# #--------------------
# #--- cartesian coords
# #--------------------
# swarm_lohi = GetCartesian( swarm_lohi )
# #--- plot arrows
# exponent = 4
# for ii in xrange(1):
# #--- setup
# fig = plt.figure(figsize=(8,8)) #,frameon=False) #, dpi=300)
# ax = fig.add_subplot(111)
# #--- xlimit
# xmin = swarm_lohi['longitude'].min()
# xmax = swarm_lohi['longitude'].max()
# ymin = swarm_lohi['latitude'].min()
# ymax = swarm_lohi['latitude'].max()
# ax.tick_params(axis='x', labelsize=14)
# ax.tick_params(axis='y', labelsize=14)
# #--- plot all events
# ax.scatter(swarm_lohi['longitude'], swarm_lohi['latitude'], # 'x(km)'],swarm_lohi['y(km)'],
# s=exponent**swarm_lohi['magnitude'],
# alpha=0.1)
# # key_max = swarm_lohi.loc[nij_trig.groupby(by='Parent_id').groups.keys()]['magnitude'].sort_values(ascending=False).index[ii]
# key_max = nij_trig.groupby(by='Parent_id').count()['R'].sort_values(ascending=False).index[ii]
# dt = nij_trig[nij_trig['Parent_id']==key_max]['T'].max()
# dx = 0.1 #nij_trig[nij_trig['Parent_id']==key_max]['R'].max()
# tt = swarm_lohi['date'].loc[key_max]
# xx = swarm_lohi.loc[ key_max ][['longitude','latitude']] #[['x(km)','y(km)','z(km)']]
# PlotArrowsSpace( swarm_lohi, d_trig,
# ( tt+datetime.timedelta(days=-dt),tt+datetime.timedelta(days=+dt)),
# (xx['longitude']-dx,xx['longitude']+dx),
# (xx['latitude']-dx,xx['latitude']+dx) )
# ax.set_xlim(xx[0]-dx,xx[0]+dx)
# ax.set_ylim(xx[1]-dx,xx[1]+dx)
In [58]:
# #--- spatial clusters
# #def GetCartesian2nd( dff ):
# # df = dff.copy()
# # xlo = df['longitude'].min()
# # xhi = df['longitude'].max()
# # ylo = df['latitude'].min()
# # yhi = df['latitude'].max()
# # getDistX = lambda x: geopy.distance.vincenty( ( 0.0, xlo ), ( 0.0, x ) ).km
# # getDistY = lambda y: geopy.distance.vincenty( ( ylo, 0.0 ), ( y, 0.0 ) ).km
# # df[ 'x' ] = df[ 'longitude' ].apply( getDistX )
# # df[ 'y' ] = df[ 'latitude' ].apply( getDistY )
# # return df
# def PlotMap(df_complete,TRIG_ID, (tmin,tmax), (xmin,xmax), (ymin,ymax) ):
# #--- plot
# counter = 0
# exponent=4
# for triggerID,colin in zip(TRIG_ID,colors):
# t0 = df_complete['date'].iloc[ triggerID ]
# # if not ( Inside(t0,(tmin,tmax) ) and
# # Inside(df_complete['y(m)'].iloc[triggerID],(xmin,xmax)) and
# # Inside(df_complete['z(m)'].iloc[triggerID],(ymin,ymax)) ):
# # continue
# counter += 1
# if counter > 10:
# break
# #--- plot
# fig = plt.figure(figsize=(5,5))#,dpi=150)
# ax = fig.add_subplot(111)
# # plt.xlim(xmin,xmax)
# # plt.ylim(ymin,ymax)
# plt.tick_params(axis='x', labelsize=14)
# plt.tick_params(axis='y', labelsize=14)
# plt.scatter(df_complete.loc[triggerID]['x(km)'],
# df_complete.loc[triggerID]['y(km)'],
# s=exponent**df_complete.loc[triggerID]['magnitude'],
# facecolors='white',color='white')
# d={'x':[],'y':[],'m':[],'t':[]}
# #--- plot daughters
# for daughter_id in d_trig[triggerID]:
# t1 = df_complete['date'].iloc[ daughter_id ]
# # if not ( Inside(t1,(tmin,tmax) ) and
# # Inside(df_complete['y(m)'].iloc[daughter_id],(xmin,xmax)) and
# # Inside(df_complete['z(m)'].iloc[daughter_id],(ymin,ymax)) ):
# # continue
# #--- remove pairs with r > cs.t
# # if rmat[ triggerID, daughter_id ] > cs * tmat[ triggerID, daughter_id ]:
# # print 'hello!'
# # continue
# d['t'].append( t1 )
# d['x'].append(df_complete['x(km)'].iloc[daughter_id])
# d['y'].append(df_complete['y(km)'].iloc[daughter_id])
# d['m'].append(df_complete['magnitude'].iloc[daughter_id])
# df=pd.DataFrame(d)
# plt.scatter(df['x'],df['y'],
# s=exponent**df['m'],
# c=df['t'], cmap='jet') #,alpha=0.1)
# plt.colorbar()
# #--- plot mother
# plt.scatter(df_complete['x(km)'].iloc[triggerID],df_complete['y(km)'].iloc[triggerID],
# s=exponent**df_complete['magnitude'].iloc[triggerID],
# marker='*',
# facecolors='yellow',color='black',
# alpha=1.0)
# #---
# colors = itertools.cycle(["r", "b", "g","b"])
# #cs = 3 * (24*3600) #--- km per day
# #--- sort
# new_list = [[len(d_trig[triggerID]),triggerID] for triggerID in d_trig]
# new_list.sort(reverse=True)
# TRIG_ID = [i[1] for i in new_list]
# #--- xlimit
# swarm_lohi=GetCartesian(swarm_lohi)
# #swarm_lohi['y(m)']=swarm_lohi['x']
# #swarm_lohi['z(m)']=swarm_lohi['y']
# xmin = swarm_lohi['x(km)'].min()
# xmax = swarm_lohi['x(km)'].max()
# ymin = swarm_lohi['y(km)'].min()
# ymax = swarm_lohi['y(km)'].max()
# #plt.tick_params(axis='x', labelsize=14)
# #plt.tick_params(axis='y', labelsize=14)
# #--- plot arrows
# PlotMap( swarm_lohi, TRIG_ID,
# # (pd.to_datetime('2010-04-04'),pd.to_datetime('2010-06-26')),
# # (pd.to_datetime('2010-04-08'),pd.to_datetime('2010-04-14')),
# ( swarm['date'].min(), swarm['date'].max()),
# (xmin,xmax),
# (ymin,ymax) )
In [59]:
#--- cluster life time
def GetPairsWithSpecifiedParentMag((m0,m1),catalog,df):
df_parents = df.groupby(by='Parent_id').groups #--- parent events
ds = catalog['magnitude'].loc[df_parents.keys()] #--- mag. of parent events
ds_m=ds[(m0 <= ds) & (ds < m1)] #--- parent events with m0<m<m1
df_m=df[pd.DataFrame([df['Parent_id'] ==k for k in ds_m.index]).any()] #--- data frame
return df_m
#def AddDist( df_trig, df_complete ):
# x=df_complete.loc[ df_trig['Event_id'] ]['r(m)']
# y=df_complete.loc[ df_trig['Parent_id'] ]['r(m)']
# df_trig['R'] = pd.Series(numpy.linalg.norm(x-y)))
# assert len ( df_trig[ df_trig['R'] == 0.0 ] ) == 0, '%s'%display( df_trig[ df_trig['R'] == 0.0 ] )
def AddTime( df_trig, df_complete ):
prefact = 1.0 / ( 24.0 * 60 * 60 ) #--- daily
x=df_complete.loc[ df_trig['Event_id'] ]
y=df_complete.loc[ df_trig['Parent_id'] ]
x.reset_index(inplace=True)
y.reset_index(inplace=True)
df_trig['T'] = x['date']-y['date']
df_trig['T'] = df_trig['T'].apply(lambda x: x.total_seconds() * prefact)
def RemovePair( df, cs ):
return df [ df[ 'R' ] <= df[ 'T' ] * cs ]
#--------------------
#----- subset (the same as trig. analysis)
#--------------------
swarm_lohi = DataFrameSubSet( swarm, #--- complete catalog
'magnitude',
( mc, sys.maxint ) )
swarm_lohi.reset_index(inplace=True,drop=True)
#--- choose m0<m<m1
n = 7
#m = list(np.linspace(mc,swarm['magnitude'].max(),n))
m_parents = swarm_lohi.loc[nij_trig.groupby(by='Parent_id').groups.keys()]['magnitude']
m = list(np.linspace(m_parents.min()-1e-6,m_parents.max()+1e-6,n))
#m+=[swarm['magnitude'].max()]
X={}
rho_dict={}
m_range={}
Err={}
fig = plt.figure(figsize=(4,4))
ax = fig.add_subplot(111)
for i in xrange( len(m) - 1 ):
m0 = m[ i ]
m1 = m[ i + 1 ]
# print m0, m1
# nij_trig.groupby(by='Parent_id')
df_trig = GetPairsWithSpecifiedParentMag((m0,m1),swarm_lohi,nij_trig) #--- get parent with m0<m<m1
df_trig.reset_index( inplace = True, drop = True )
#--- add distance & time column
# df_trig['R'] = rmat[df_trig['Parent_id'],df_trig['Event_id']]
# df_trig['T'] = tmat[df_trig['Parent_id'],df_trig['Event_id']]
# assert len ( df_trig[ df_trig['R'] == 0.0 ] ) == 0, '%s'%display( df_trig[ df_trig['R'] == 0.0 ] )
# assert len ( df_trig[ df_trig['T'] == 0.0 ] ) == 0, '%s'%display( df_trig[ df_trig['T'] == 0.0 ] )
#--- remove pairs with r > cs.t
# cs = 3 * (24*3600) #--- km per day
# df_trig = RemovePair( df_trig, cs )
#--- life time
df_duration = df_trig.groupby(by='Parent_id')['T'].max()
#--- rho plots
n_decades = int( math.ceil( log(df_duration.max()/df_duration.min(),10) ) )
nbin_per_decade = 3
nbins = nbin_per_decade * n_decades
rho, xedges=np.histogram(df_duration,
density=True,
bins=np.logspace(log(df_duration.min(),10),
log(df_duration.max(),10),nbins))
hist, xedges=np.histogram(df_duration,
bins=np.logspace(log(df_duration.min(),10),
log(df_duration.max(),10),nbins))
err = rho/np.sqrt(hist)
#--- rho
# plt.xlim(1e-3,1e2)
# plt.ylim(1e-3,1e2)
plt.xscale('log')
plt.yscale('log')
plt.xlabel('Duration(Day)')
plt.ylabel('P(Duration)')
plt.errorbar(xedges[:-1],rho, yerr=err,label='[%2.1f,%2.1f]'%(m0,m1))
fontP = FontProperties()
fontP.set_size('small')
plt.legend(title='m',prop=fontP,loc='upper right',bbox_to_anchor=(1.5, 1))
x=xedges[:-1]
X[i] = x[:]
rho_dict[i]=rho[:]
m_range[i]=np.array([m0,m1])
Err[i]=err[:]
#plt.savefig('%s/duration.png'%DIR_OUTPT_figs,dpi=75,bbox_inches='tight')
In [60]:
#--- histograms: magnitude of mother events
#--------------------
#----- subset (the same as trig. analysis)
#--------------------
swarm_lohi = DataFrameSubSet( swarm, #--- complete catalog
'magnitude',
( mc, sys.maxint ) )
swarm_lohi.reset_index(inplace=True,drop=True)
mlist = swarm_lohi.loc[ nij_trig.groupby(by='Parent_id').groups.keys() ]['magnitude']
#plt.hist(mlist)
list_of_zero_afs = set(df_trig['Event_id'])-set(df_trig['Parent_id'])
df_zeros = pd.Series(np.zeros(len(list_of_zero_afs)),index=list_of_zero_afs)
mlist0= swarm_lohi['magnitude'].loc[df_zeros.index]
#--- accumulated histogram
N = len(mlist)+len(mlist0)
slist=mlist.tolist()+mlist0.tolist() #np.array(swarm_copy['magnitude'])
slist.sort()
d = histogramACCUMLTD( slist )
keys=d.keys()
keys.sort()
#--- plot
fig, ax = plt.subplots(figsize=(4,4))
ax.set_yscale('log')
ax.set_xlabel('$m$')
ax.set_ylabel('$N(m)$')
xmin=min(slist)
xmax=max(slist)
ax.axis([xmin,xmax,1,1000])
#ax.set_xticks(np.linspace(1,6,6))
dx=0.1
junk = ax.hist( slist,
bins=int((xmax-xmin)/dx),
label='histogram',color='silver') #--- histogram
xx=[];yy=[]
for ikey in keys:
xx.append(d[ikey][0])
yy.append(N-d[ikey][2])
ax.plot(xx,yy,
linestyle='-', drawstyle='steps-post',color='black',
linewidth=1.0) #--- accumulated
b=1.65
ax.plot([xmin,xmax],
[1e3, 1e3* 10**(-b*(xmax-xmin))],'r-.',linewidth=1)
#DrawFrame(ax, (0.2,0.06),(0.14,0.06),0.1,LOG_Y=True)
#plt.savefig('%s/gr.png'%DIR_OUTPT_figs,dpi=300,bbox_inches='tight',transparent=True)
Out[60]:
In [61]:
#--- productivity relation
mpl.rcParams.update(mpl.rcParamsDefault)
warnings.filterwarnings('ignore') #--- get rid of warnings
rc('text', usetex=True)
font = {'size' : 26}
matplotlib.rc('font', **font)
import numpy as np
import math
def GetPairsWithSpecifiedParentMag((m0,m1),catalog,df):
df_parents = df.groupby(by='Parent_id').groups #--- parent events
ds = catalog['magnitude'].loc[df_parents.keys()] #--- mag. of parent events
ds_m=ds[(m0 <= ds) & (ds < m1)] #--- parent events with m0<m<m1
df_m=df[pd.DataFrame([df['Parent_id'] ==k for k in ds_m.index]).any()] #--- data frame
return df_m, np.mean( ds_m ), np.std( ds_m )/(len(ds_m))**0.5 #--- exponential: std=mean
#def AddDist( df_trig, df_complete ):
# x=df_complete.loc[ df_trig['Event_id'] ]['r(m)']
# y=df_complete.loc[ df_trig['Parent_id'] ]['r(m)']
# df_trig['R'] = pd.Series(numpy.linalg.norm(x-y)))
# assert len ( df_trig[ df_trig['R'] == 0.0 ] ) == 0, '%s'%display( df_trig[ df_trig['R'] == 0.0 ] )
def AddTime( df_trig, df_complete ):
prefact = 1.0 / ( 24.0 * 60 * 60 ) #--- daily
x=df_complete.loc[ df_trig['Event_id'] ]
y=df_complete.loc[ df_trig['Parent_id'] ]
x.reset_index(inplace=True)
y.reset_index(inplace=True)
df_trig['T'] = x['date']-y['date']
df_trig['T'] = df_trig['T'].apply(lambda x: x.total_seconds() * prefact)
def RemovePair( dff, cs ):
df = dff.copy()
df['R'] = rmat[df['Parent_id'],df['Event_id']]
df['T'] = tmat[df['Parent_id'],df['Event_id']]
assert len ( df[ df['R'] == 0.0 ] ) == 0, '%s'%display( df[ df['R'] == 0.0 ] )
assert len ( df[ df['T'] == 0.0 ] ) == 0, '%s'%display( df[ df['T'] == 0.0 ] )
return df [ df[ 'R' ] <= df[ 'T' ] * cs ]
def AdjustBins(data,bins):
hist, xedges=np.histogram(data, #--- histogram
bins=bins)
tmp = [xedges[0]]
for i,j in zip(xedges[1:],hist): #--- expand bins
if j < 2:
continue
tmp.append(i)
# tmp.append(xedges[-1])
if hist[-1] < 2:
tmp.pop(-2)
return tmp
def GetParentsMagnitudes( swarm_lohi, df_trig ):
mlist = swarm_lohi.loc[ df_trig.groupby(by='Parent_id').groups.keys() ]['magnitude']
list_of_zero_afs = set(df_trig['Event_id'])-set(df_trig['Parent_id'])
df_zeros = pd.Series(np.zeros(len(list_of_zero_afs)),index=list_of_zero_afs)
mlist0= swarm_lohi['magnitude'].loc[df_zeros.index]
return mlist.tolist()+mlist0.tolist()
#--------------------
#----- subset (the same as trig. analysis)
#--------------------
swarm_lohi = DataFrameSubSet( swarm, #--- complete catalog
'magnitude',
( mc, sys.maxint ) )
swarm_lohi.reset_index(inplace=True,drop=True)
#--- remove pairs with r > cs.t
#cs = 3 * (24*3600) #--- km per day
df_trig = nij_trig.copy()
#--- parents' magnitudes
m_list = GetParentsMagnitudes( swarm_lohi, df_trig )
#--- number of daughters for each mother
df_nn = df_trig.groupby(by='Parent_id').count()['Event_id']
#--- include daughters with zero children
list_of_zero_afs = set(df_trig['Event_id'])-set(df_trig['Parent_id'])
df_zeros = pd.Series(np.zeros(len(list_of_zero_afs)),index=list_of_zero_afs)
#--- scattered plot
fig = plt.figure(figsize=(4,4),frameon=True)
ax = fig.add_subplot(111)
#ax.set_xlim(mc,swarm_lohi['magnitude'].max()+0.5)
m_min = min(m_list)-1.0e-6
m_max = max(m_list)+1.0e-6
ax.set_xlim(np.floor(m_min),np.ceil(m_max))
ax.set_ylim(0.2,10**np.ceil(np.log10(df_nn.max())))
ax.set_yscale('log')
ax.plot( swarm_lohi['magnitude'].loc[df_nn.index],
df_nn,
'x',color='black',alpha=0.25,zorder=1,label='')
ax.legend(fontsize=0)
ax2=ax.twinx()
ax2.set_yscale('linear')
ax2.set_xlim(np.floor(m_min),np.ceil(m_max))
ax2.set_ylim(-.02,1)
ax2.plot( swarm_lohi['magnitude'].loc[df_zeros.index],
df_zeros,
'x',color='black',alpha=0.25)
ax2.tick_params(labelright=False,labelleft=False,left=False, right=False)
#plt.yscale('log')
#plt.xlabel('$m$')
#plt.ylabel(r'$N_{as}$')
ax.tick_params(axis='y',left=True, right=True,which='both')
ax.tick_params(axis='x',bottom=True, top=True,which='both')
#--- choose m0<m<m1
dm = 0.1
n = int( ( m_max - m_min ) / dm )
m = list(np.linspace(m_min,m_max,n))
m=AdjustBins(m_list,m)
Mlist=m
m_mean=np.array(np.zeros(len(m) - 1))
m_err=np.array(np.zeros(len(m) - 1))
N_as = np.array(np.zeros(len(m) - 1))
err_N = np.array(np.zeros(len(m) - 1))
for i in xrange( len(m) - 1 ):
try:
m0 = m[ i ]
m1 = m[ i + 1 ]
df, m_mean[ i ], m_err[i] = GetPairsWithSpecifiedParentMag((m0,m1),
swarm_lohi,df_trig) #--- get parent with m0<m<m1
df.reset_index( inplace = True, drop = True )
#--- number of daughters for each mother
df_n = df.groupby(by='Parent_id').count()['Event_id']
#--- include daughters with zero children
list_of_zero_afs = set(df_trig['Event_id'])-set(df_trig['Parent_id'])
subset = swarm_lohi.loc[list_of_zero_afs]
list_of_zero_afs = subset[(subset['magnitude'] >= m0) & (subset['magnitude'] <= m1)].index
df_zeros = pd.Series(np.zeros(len(list_of_zero_afs)),index=list_of_zero_afs)
N_as[ i ] = 1.0*(df_n.sum()+ df_zeros.sum())/(len(df_n)+len(df_zeros))
err_N[ i ] = (N_as[ i ]/(len(df_n)+len(df_zeros)))**0.5 #--- poisson
# err_N[ i ]=np.std(df_n.tolist()+df_zeros.tolist())/(len(df_n)+len(df_zeros))**0.5
except:
print traceback.print_exc()
continue
#ax.plot(m, np.append(N_as,N_as[-1]), linestyle='-', drawstyle='steps-post',color='red')
ax.errorbar(m_mean,N_as,
yerr=err_N,xerr=m_err,
markerfacecolor='white',
fmt='o', markersize=8,color='red',markeredgewidth=0.7,
linewidth=.5,
barsabove=None,capsize=5,capthick=1,elinewidth=1,
zorder=2)
#--- add major xticks
xmin=np.ceil(ax.axis()[0])
xmax=np.floor(ax.axis()[1])
nbin = xmax - xmin
ax.set_xticks(np.linspace(xmin,xmax,int(nbin)+1))
DrawFrame(ax, (0.24,0.08),(0.14,0.06),0.01,LOG_Y=True)
#from scipy.optimize import curve_fit
def func(x,alpha,c):
return c*10**(alpha*x)
#popt, pconv = curve_fit(func,m_mean,N_as)
popt = np.polyfit(m_mean,np.log10(N_as), 1)
popt[1] = 10**(popt[1])
alpha_p = popt[0]
mm = swarm_lohi['magnitude'].loc[df_zeros.index].tolist() + \
swarm_lohi['magnitude'].loc[df_nn.index].tolist() #swarm_lohi[swarm_lohi['magnitude']>=mc]['magnitude']
mm = np.array(mm)
mm=list(set(mm))
mm.sort()
mm=np.array(mm)
ax.plot(mm,func(mm,*popt),'-.g',zorder=3,label='$N\propto 10^{%3.2f m}$'%popt[0])
ax.legend(fontsize='xx-small',frameon=False)
ax.set_title('$q=%d,d_f=%s$'%(quantile*100,Df),fontsize='xx-small')
#print 'alpha=%s'%popt[0]
#print pconv**0.5
plt.savefig('%s/prod.png'%DIR_OUTPT_figs,dpi=75*.75,bbox_inches='tight')
mpl.rcParams.update(mpl.rcParamsDefault)
warnings.filterwarnings('ignore') #--- get rid of warnings
rc('text', usetex=True)
font = {'size' : 20 }
matplotlib.rc('font', **font)
np.save('%s/alpha'%DIR_OUTPT_figs,alpha_p)
plt.show()
multiple realizations¶
In [62]:
from IPython.display import Image
alpha_arr=[]
for irun in xrange(16):
path = 'runFillmore/Run%s'%irun
a=np.load('%s/alpha.npy'%path)
alpha_arr.append(a.item())
#--- load image
display(Image(filename='%s/prod.png'%path))
df=pd.DataFrame({'mean':[np.mean(alpha_arr)],'std_dev':np.std(alpha_arr),
'std_err':[np.std(alpha_arr)/len(alpha_arr)**.5]},
index=[r'$\alpha$'])
display(df)
df['mean']+2*df['std_dev'],df['mean']-2*df['std_dev']
In [63]:
#--- number distributions
#--------------------
#----- subset (the same as trig. analysis)
#--------------------
swarm_lohi = DataFrameSubSet( swarm, #--- complete catalog
'magnitude',
( mc, sys.maxint ) )
swarm_lohi.reset_index(inplace=True,drop=True)
#--- remove pairs with r > cs.t
#cs = 3 * (24*3600) #--- km per day
df_trig = nij_trig.copy()
#--- parents' magnitudes
m_list = GetParentsMagnitudes( swarm_lohi, df_trig )
#--- number of daughters for each mother
df_nn = df_trig.groupby(by='Parent_id').count()['Event_id']
#--- include daughters with zero children
list_of_zero_afs = set(df_trig['Event_id'])-set(df_trig['Parent_id'])
df_zeros = pd.Series(np.zeros(len(list_of_zero_afs)),index=list_of_zero_afs)
#--- scattered plot
fig = plt.figure(figsize=(4,4),frameon=True)
ax = fig.add_subplot(111)
ax.plot( swarm_lohi['magnitude'].loc[df_nn.index],
df_nn,
'x',color='gray',alpha=1.0)
ax.plot( swarm_lohi['magnitude'].loc[df_zeros.index],
df_zeros,
'x',color='gray')
ax.set_yscale('log')
#--- parents' magnitudes
m_list = GetParentsMagnitudes( swarm_lohi, df_trig )
#--- number of daughters for each mother
df_nn = df_trig.groupby(by='Parent_id').count()['Event_id']
#--- include daughters with zero children
list_of_zero_afs = set(df_trig['Event_id'])-set(df_trig['Parent_id'])
df_zeros = pd.Series(np.zeros(len(list_of_zero_afs)),index=list_of_zero_afs)
#--- scattered plot
m_min = min(m_list)-1e-6 #0.05 #-1.0e-6
m_max = max(m_list)+1.0e-6 #3.299999333333333 #max(m_list)+0.05 #+1.0e-6 #--- exclude the largest event
#--- choose m0<m<m1
dm = 0.4
n = int( ( m_max - m_min ) / dm )
m = [m_min,m_max] #list(np.linspace(m_min,m_max,n+1))
Mlist=m
m_mean=np.array(np.zeros(len(m) - 1))
m_err=np.array(np.zeros(len(m) - 1))
N_as = np.array(np.zeros(len(m) - 1))
err_N = np.array(np.zeros(len(m) - 1))
for i in xrange(len(m) - 1 ):
try:
m0 = m[ i ]
m1 = m[ i + 1 ]
df, m_mean[ i ], m_err[i] = GetPairsWithSpecifiedParentMag((m0,m1),
swarm_lohi,df_trig) #--- get parent with m0<m<m1
df.reset_index( inplace = True, drop = True )
#--- number of daughters for each mother
df_n = df.groupby(by='Parent_id').count()['Event_id']
#--- include daughters with zero children
list_of_zero_afs = set(df_trig['Event_id'])-set(df_trig['Parent_id'])
subset = swarm_lohi.loc[list_of_zero_afs]
list_of_zero_afs = subset[(subset['magnitude'] >= m0) & (subset['magnitude'] <= m1)].index
df_zeros = pd.Series(np.zeros(len(list_of_zero_afs)),index=list_of_zero_afs)
# fig.hist(df_n)
# if m1 > 3.3:
# continue
fig = plt.figure(figsize=(4,4),frameon=True)
ax = fig.add_subplot(111)
junk = ax.hist( df_n.tolist()+df_zeros.tolist(),
bins=1024,#int((xmax-xmin)/dx),
label='%3.2f-%3.2f'%(m0,m1),color='silver') #--- histogram
print '#=',junk[0][junk[0]!=0]
print 'N=',junk[1][:-1][junk[0]!=0]
ax.set_xlabel('$N_{as}$')
ax.set_ylabel('number')
# ax.set_ylim(-100,ax.axis[3])
fig.legend()
#--- mean
# print [m0,m1],list_of_zero_afs
# pdb.set_trace()
print 'n_ms=',len(df_n)#+len(df_zeros)
print 'n_ms(0)=',len(df_zeros)
N_as[ i ] = 1.0*(df_n.sum()+ df_zeros.sum())/(len(df_n)+len(df_zeros))
err_N[ i ] = (N_as[ i ]/(len(df_n)+len(df_zeros)))**0.5 #--- poisson
# err_N[ i ]=np.std(df_n.tolist()+df_zeros.tolist())/(len(df_n)+len(df_zeros))**0.5
except:
continue
In [64]:
#--- choose bins for rho and lambda
import traceback
#--------------------
#----- subset (the same as trig. analysis)
#--------------------
swarm_lohi = DataFrameSubSet( swarm, #--- complete catalog
'magnitude',
( mc, sys.maxint ) )
swarm_lohi.reset_index(inplace=True,drop=True)
#--- remove pairs with r > cs.t
#cs = 3 * (24*3600) #--- km per day
df_trig = nij_trig.copy()
#--- parents' magnitudes
m_list = GetParentsMagnitudes( swarm_lohi, df_trig )
#--- number of daughters for each mother
df_nn = df_trig.groupby(by='Parent_id').count()['Event_id']
#--- include daughters with zero children
list_of_zero_afs = set(df_trig['Event_id'])-set(df_trig['Parent_id'])
df_zeros = pd.Series(np.zeros(len(list_of_zero_afs)),index=list_of_zero_afs)
#--- scattered plot
fig = plt.figure(figsize=(4,4),frameon=True)
ax = fig.add_subplot(111)
#ax.set_xlim(mc,swarm_lohi['magnitude'].max()+0.5)
m_min = min(m_list)-1.0e-6
m_max = max(m_list)+1.0e-6 #--- exclude the largest event
ax.set_xlim(m_min,np.ceil(m_max))
ax.set_ylim(0.1,1000)
ax.plot( swarm_lohi['magnitude'].loc[df_nn.index],
df_nn,
'o',color='black',alpha=.1)
ax.plot( swarm_lohi['magnitude'].loc[df_zeros.index],
df_zeros,
'x',color='gray')
plt.yscale('log')
#plt.xlabel('$m$')
#plt.ylabel(r'$N_{as}$')
#--- choose m0<m<m1
dm = 0.75 #0.5
n = int( (6.0 - m_min ) / dm )
m = list(np.linspace(m_min,6.0,n))
#m=AdjustBins(m_list,m)
# m=[2.7999989999999997,
# 3.133332555555555,
# 3.466666111111111,
# 3.7999996666666664,
# 4.133333222222222,
# 4.466666777777778,
# 4.800000333333333,
# 5.800001]
m+=[6.41,7.1-0.01,7.1+0.01]
Mlist=m
m_mean=np.array(np.zeros(len(m) - 1))
m_err=np.array(np.zeros(len(m) - 1))
N_as = np.array(np.zeros(len(m) - 1))
err_N = np.array(np.zeros(len(m) - 1))
for i in xrange( len(m) - 1 ):
try:
m0 = m[ i ]
m1 = m[ i + 1 ]
df, m_mean[ i ], m_err[i] = GetPairsWithSpecifiedParentMag((m0,m1),
swarm_lohi,df_trig) #--- get parent with m0<m<m1
df.reset_index( inplace = True, drop = True )
# pdb.set_trace()
#--- number of daughters for each mother
df_n = df.groupby(by='Parent_id').count()['Event_id']
#--- include daughters with zero children
list_of_zero_afs = set(df_trig['Event_id'])-set(df_trig['Parent_id'])
subset = swarm_lohi.loc[list_of_zero_afs]
list_of_zero_afs = subset[(subset['magnitude'] >= m0) & (subset['magnitude'] <= m1)].index
df_zeros = pd.Series(np.zeros(len(list_of_zero_afs)),index=list_of_zero_afs)
#--- mean
# print [m0,m1],list_of_zero_afs
# pdb.set_trace()
N_as[ i ] = 1.0*(df_n.sum()+ df_zeros.sum())/(len(df_n)+len(df_zeros))
err_N[ i ] = (N_as[ i ]/(len(df_n)+len(df_zeros)))**0.5 #--- poisson
# err_N[ i ]=np.std(df_n.tolist()+df_zeros.tolist())/(len(df_n)+len(df_zeros))**0.5
except:
# traceback.print_exc()
continue
#ax.plot(m, np.append(N_as,N_as[-1]), linestyle='-', drawstyle='steps-post',color='red')
ax.errorbar(m_mean,N_as,
yerr=err_N,xerr=m_err,
markerfacecolor='white',
fmt='o', markersize=8,color='red',markeredgewidth=0.7,
linewidth=.5,
barsabove=None,capsize=5,capthick=1,elinewidth=1)
#--- add major xticks
xmin=np.ceil(ax.axis()[0])
xmax=np.floor(ax.axis()[1])
nbin = xmax - xmin
ax.set_xticks(np.linspace(xmin,xmax,int(nbin)+1))
DrawFrame(ax, (0.15,0.08),(0.14,0.06),0.1,LOG_Y=True)
try:
from scipy.optimize import curve_fit
def func(x,c,alpha):
return c*10**(alpha*x)
popt, pconv = curve_fit(func,m_mean[m_mean>=mc],N_as[m_mean>=mc])
mm = swarm_lohi['magnitude'].loc[df_zeros.index].tolist() + \
swarm_lohi['magnitude'].loc[df_nn.index].tolist() #swarm_lohi[swarm_lohi['magnitude']>=mc]['magnitude']
mm = np.array(mm)
mm=list(set(mm))
mm.sort()
mm=np.array(mm)
ax.plot(mm,func(mm,*popt),'-.g')
print popt
print pconv**0.5
except:
pass
#plt.savefig('%s/prod.png'%DIR_OUTPT_figs,dpi=150,bbox_inches='tight')
fig = plt.figure(figsize=(4,4),frameon=True)
ax = fig.add_subplot(111)
ax.plot(m, np.append(N_as,N_as[-1]), linestyle='-', drawstyle='steps-post',color='red')
ax.errorbar(m_mean,N_as,
yerr=err_N,xerr=m_err,
markerfacecolor='white',
fmt='o', markersize=8,color='red',markeredgewidth=0.7,
linewidth=.5,
barsabove=None,capsize=5,capthick=1,elinewidth=1)
ax.set_xlim(m_min,np.ceil(m_max))
ax.set_ylim(0.1,1000)
ax.set_yscale('log')
ax.set_xticks(np.linspace(xmin,xmax,int(nbin)+1))
plt.show()
In [65]:
m
Out[65]:
In [66]:
#--- density plots: rho(r)
#--- split based on the mainshock's magnitude
import numpy as np
import math
#def AdjustBins(data,bins):
# hist, xedges=np.histogram(data, #--- histogram
# bins=bins)
# tmp = [xedges[0]]
# for i,j in zip(xedges[1:],hist): #--- expand bins
# if j < 2:
# continue
# tmp.append(i)
# tmp.append(xedges[-1])
# if hist[-1] < 2:
# tmp.pop(-2)
# return tmp
#def GetPairsWithSpecifiedParentMag((m0,m1),catalog,df):
# df_parents = df.groupby(by='Parent_id').groups #--- parent events
# ds = catalog['magnitude'].loc[df_parents.keys()] #--- mag. of parent events
# ds_m=ds[(m0 <= ds) & (ds < m1)] #--- parent events with m0<m<m1
# df_m=df[pd.DataFrame([df['Parent_id'] ==k for k in ds_m.index]).any()] #--- data frame
# return df_m, np.mean( ds_m )
#def AddDist( df_trig, df_complete ):
# x=df_complete.loc[ df_trig['Event_id'] ]['r(m)']
# y=df_complete.loc[ df_trig['Parent_id'] ]['r(m)']
# df_trig['R'] = pd.Series(numpy.linalg.norm(x-y)))
# assert len ( df_trig[ df_trig['R'] == 0.0 ] ) == 0, '%s'%display( df_trig[ df_trig['R'] == 0.0 ] )
def AddTime( df_trig, df_complete ):
prefact = 1.0 / ( 24.0 * 60 * 60 ) #--- daily
x=df_complete.loc[ df_trig['Event_id'] ]
y=df_complete.loc[ df_trig['Parent_id'] ]
x.reset_index(inplace=True)
y.reset_index(inplace=True)
df_trig['T'] = x['date']-y['date']
df_trig['T'] = df_trig['T'].apply(lambda x: x.total_seconds() * prefact)
def RemovePair( df, cs ):
return df [ df[ 'R' ] <= df[ 'T' ] * cs ]
#--------------------
#----- subset (the same as trig. analysis)
#--------------------
swarm_lohi = DataFrameSubSet( swarm, #--- complete catalog
'magnitude',
( mc, sys.maxint ) )
swarm_lohi.reset_index(inplace=True,drop=True)
##--- parents' magnitudes
#df_trig = nij_trig.copy()
#m_list = GetParentsMagnitudes( swarm_lohi, df_trig )
#m_min = min(m_list)-1.0e-6
#m_max = max(m_list)+1.0e-6 #--- exclude the largest event
#
##--- choose m0<m<m1
#dm = 0.3
#n = int( ( m_max - m_min ) / dm )
#m = list(np.linspace(m_min,m_max,n))
#m=AdjustBins(m_list,m)
Mlist=m
#--- choose m0<m<m1
X={}
rho_dict={}
m_range={}
Err={}
m_mean={}
for i in xrange( len(m) - 1 ):
try:
m0 = m[ i ]
m1 = m[ i + 1 ]
df_trig, m_mean[ i ],junk = GetPairsWithSpecifiedParentMag((m0,m1),swarm_lohi,nij_trig) #--- get parent with m0<m<m1
df_trig.reset_index( inplace = True, drop = True )
#--- add distance & time column
# AddDist( df_trig, df_complete )
# df_trig['R'] = rmat[df_trig['Parent_id'],df_trig['Event_id']]
# df_trig['T'] = tmat[df_trig['Parent_id'],df_trig['Event_id']]
# assert len ( df_trig[ df_trig['R'] == 0.0 ] ) == 0, '%s'%display( df_trig[ df_trig['R'] == 0.0 ] )
# AddTime( df_trig, df_complete )
#--- remove pairs with r > cs.t
# cs = 3 * (24*3600) #--- km per day
# df_trig = RemovePair( df_trig, cs )
#--- rho plots
n_decades = int( math.ceil( log(df_trig['R'].max()/df_trig['R'].min(),10) ) )
nbin_per_decade = 4
nbins = nbin_per_decade * n_decades
bins = np.logspace(log(df_trig['R'].min(),10)-1.e-10,
log(df_trig['R'].max(),10)+1.e-10,nbins)
bins = AdjustBins(df_trig['R'],bins)
rho, xedges=np.histogram(df_trig['R'],
density=True,
bins=bins)
hist, xedges=np.histogram(df_trig['R'],
bins=bins)
x_bins, junk=np.histogram(df_trig['R'], #--- histogram
bins=bins,
weights = df_trig['R'])
#--- rm empty bins
x_bins = x_bins[ hist != 0 ]
rho = rho[ hist != 0 ]
hist = hist[ hist != 0 ]
#--- poisson err
err = rho/np.sqrt(hist)
x_bins /= hist
#--- scattered plot
fig=plt.figure(figsize=(8,4))
ax=fig.add_subplot(1,2,1)
ax.set_title('$%2.1f<m<%2.1f$'%(m0,m1))
ax.set_xscale('log')
ax.set_yscale('log')
ax.set_xlabel('$t$')
ax.set_ylabel('$r$')
ax.set_xlim(1e-5,10)
ax.set_ylim(1e-4,1e2)
ax.scatter(df_trig['T'],df_trig['R'],alpha=0.1)
#--- discretization effects
# dt_min=df_trig['T'].min()
# dt_max=df_trig['T'].max()
# dr_min=df_trig['R'].min()
# dr_max=df_trig['R'].max()
# ax.plot([dt_min,dt_min],[dr_min,dr_max],
# '-',color='blue')
# ax.plot([dt_max,dt_max],[dr_min,dr_max],
# '-',color='blue')
# ax.plot([dt_min,dt_max],[dr_min,dr_min],
# '-',color='blue')
# ax.plot([dt_min,dt_max],[dr_max,dr_max],
# '-',color='blue')
# ax.set_ylim(dr_min/2,dr_max*2)
# ax.plot([dt_min,dt_max],[dt_min*cs,dt_max*cs],
# '-',color='red')
#--- rho
ax=fig.add_subplot(1,2,2)
ax.set_xlim(1e-4,1e2)
ax.set_ylim(1e-5,1e1)
ax.set_xscale('log')
ax.set_yscale('log')
ax.set_xlabel('$r$')
ax.set_ylabel('$P(r)$')
ax.errorbar(x_bins,rho, yerr=err)
X[i] = x_bins[:]
rho_dict[i]=rho[:]
m_range[i]=np.array([m0,m1])
Err[i]=err[:]
# plt.savefig('%s/rho_r.%s.png'%(DIR_OUTPT_figs,i),dpi=50,bbox_inches='tight')
except:
continue
plt.show()
rupture length¶
In [67]:
#--- density plots: rho(r)
#--- split based on the mainshock's magnitude
import numpy as np
import math
#--------------------
#----- subset (the same as trig. analysis)
#--------------------
swarm_lohi = DataFrameSubSet( swarm, #--- complete catalog
'magnitude',
( mc, sys.maxint ) )
swarm_lohi.reset_index(inplace=True,drop=True)
XX={}
rho_dictt={}
Errr={}
m_meann={}
r_rupp = {}
groups_dic=nij_trig.groupby(by='Parent_id').groups
for parent_id in groups_dic:
# print parent_id
df_trig = nij_trig.loc[groups_dic[parent_id]]
df_trig.reset_index( inplace = True, drop = True )
# display(df_trig )
if len(df_trig) < 2:
continue
#--- rho plots
n_decades = int( math.ceil( log(df_trig['R'].max()/df_trig['R'].min(),10) ) )
nbin_per_decade = 4
nbins = nbin_per_decade * n_decades
bins = np.logspace(log(df_trig['R'].min(),10)-1.e-10,
log(df_trig['R'].max(),10)+1.e-10,nbins)
# bins = AdjustBins(df_trig['R'],bins)
rho, xedges=np.histogram(df_trig['R'],
density=True,
bins=bins)
hist, xedges=np.histogram(df_trig['R'],
bins=bins)
x_bins, junk=np.histogram(df_trig['R'], #--- histogram
bins=bins,
weights = df_trig['R'])
#--- rm empty bins
x_bins = x_bins[ hist != 0 ]
rho = rho[ hist != 0 ]
hist = hist[ hist != 0 ]
#--- poisson err
err = rho/np.sqrt(hist)
x_bins /= hist
i = parent_id
XX[i] = x_bins[:]
rho_dictt[i]=rho[:]
m_meann[i]=swarm_lohi['magnitude'].loc[i]
Errr[i]=err[:]
r_rupp[i]=np.std(df_trig['R'])
m_meann=pd.Series(m_meann)
r_rupp=pd.Series(r_rupp)
#--- fit
def func(x,alpha,c):
return c*10**(alpha*x)
popt = np.polyfit(m_meann,np.log10(r_rupp), 1)
popt[1] = 10**(popt[1])
#--- plot
fig = plt.figure(figsize=(4,4))
ax=fig.add_subplot(111)
#ax.set_xscale('log')
ax.set_yscale('log')
ax.set_xlabel('$m$')
ax.set_ylabel('$r_{rup}$[km]')
#ax.set_xlim(2,6)
#ax.set_ylim(1e-4,1e2)
ax.scatter(m_meann,r_rupp,alpha=0.2)
ax.plot(m_meann,func(m_meann,*popt),'-.r',zorder=3,
label='$r_{rup}\propto 10^{%3.2f m},r_c=%3.2e$'%(popt[0],popt[1]))
ax.legend(fontsize='xx-small',frameon=False)
#ax.set_title('q=%d%%,df=%s'%(quantile*100,Df),fontsize='xx-small')
#print 'alpha=%s'%popt[0]
sigma=popt[0]
rc=popt[1] #10**np.ceil(np.log10(popt[1]))*2
####plt.savefig('%s/rupture_mag.png'%DIR_OUTPT_figs,dpi=75,bbox_inches='tight',transparent=True)
plt.show()
$r_{rup}$ by fitting¶
In [68]:
from scipy.optimize import curve_fit
#def func(x,pref, xmean,sigma):
# return pref * np.exp(-((x-xmean)/sigma)**2)
def func(x,a,b1,b2,rc):
return a*x**b1/(1.0+(x/rc)**b2)
#def func2(x,c,alpha):
# return c*10**(alpha*x)
#--- fit
def func2(x,alpha,c):
return c*10**(alpha*x)
colors = ['black','red','green','blue','cyan','brown','violet','magenta','orange','yellow']
fig=plt.figure(figsize=(8,4))
ax=fig.add_subplot(121)
#ax.axis([2e-3,2e-3*1e1/1e-3,1e-3,1e1])
ax.set_xscale('log')
ax.set_yscale('log')
ax.set_xlabel('$r$')
ax.set_ylabel('$P(r)$')
r_peak=[]
mm_mean=[]
p0 = (1.0,Df-1,2.0,rc)
xmin = ymin = sys.maxint
ymax=xmax=-sys.maxint
for key, col in zip(X,colors):
try:
# if key > 6:
# continue
# print np.mean(X[key])
if np.max(X[key]) > xmax:
xmax = np.max(X[key])
if np.min(rho_dict[key]) < ymin:
ymin = np.min(rho_dict[key])
if np.max(rho_dict[key]) > ymax:
ymax = np.max(rho_dict[key])
ax.errorbar(X[key],rho_dict[key],
yerr=Err[key],
linestyle='None', color=col,
fmt='-o', markersize=8
)
popt, pcov = curve_fit(func, X[key], rho_dict[key],
sigma=Err[key],
# bounds=((0.0,0.0,0.0), (np.inf,np.inf,np.inf)),
p0=p0
)
mm_mean+=[m_mean[key]]
p0 = popt[:]
(a,b1,b2,rc)=popt
# print b2-b1
r_peak += [rc]
ax.plot(X[key], func(X[key], *popt),'-',color=col)#,label='fit: r=%3.2f' % (popt[1]))
ax.legend()
except:
traceback.print_exc()
# print key
continue
(ylo,yhi)=(10**np.floor(np.log10(ymin)),\
10**np.ceil(np.log10(ymax)))
xhi=10**np.ceil(np.log10(xmax))
ax.axis([xhi/(yhi/ylo),xhi,ylo,yhi])
try:
ax=fig.add_subplot(122)
ax.set_yscale('log')
ax.set_xlabel('$m$')
ax.set_ylabel('$r_{rup}$')
ax.plot(mm_mean,r_peak,'o')
ylo=10**np.floor(np.log10(np.min(r_peak)))
yhi=10**np.ceil(np.log10(np.max(r_peak)))
ax.set_ylim(ylo,yhi)
#
popt = np.polyfit( mm_mean,np.log10(r_peak),1 )
sigma=popt[0]
rc=10**popt[1] #10**np.ceil(np.log10(popt[1]))
rc0=rc
#
ax.plot(mm_mean,func2( np.array(mm_mean),sigma,rc),'--r',
label='$r_{rup}\propto 10^{%3.2f m},r_c=%2.1e$'%(sigma,rc))
ax.legend(fontsize='xx-small',frameon=False)
fig.tight_layout()
except:
traceback.print_exc()
pass
ax.set_title('$q=%d,d_f=%s$'%(quantile*100,Df),fontsize='xx-small')
plt.show()
#fig.savefig('%s/r_rupt.png'%DIR_OUTPT_figs,dpi=75,bbox_inches='tight')
np.save('%s/sigma'%DIR_OUTPT_figs,sigma)
different realizations¶
In [69]:
alpha_arr=[] #---
for irun in xrange(16):
path = 'runFillmore/Run%s'%irun
a=np.load('%s/sigma.npy'%path)
alpha_arr.append(a.item())
#--- load image
display(Image(filename='%s/r_rupt.png'%path))
df=pd.DataFrame({'mean':[np.mean(alpha_arr)], 'std_dev':np.std(alpha_arr),
'std_err':[np.std(alpha_arr)/len(alpha_arr)**.5]},
index=[r'$\sigma$'])
display(df)
df['mean']+2*df['std_dev'],df['mean']-2*df['std_dev']
In [70]:
#--- density plots: rho(r) 2nd
plt.figure(figsize=(15,5))
#--- plot rho
plt.subplot(1,3,1)
plt.xscale('log')
plt.yscale('log')
plt.xlabel(r'$r$')
plt.ylabel(r'$P(r)$')
plt.xlim(1e-3,1e2)
plt.ylim(1e-4,1e1)
for key in X:
# if key < 3:
# continue
plt.errorbar(X[key],rho_dict[key],
yerr=Err[key],
fmt='-o', markersize=8
)
#--- rescaled in x and y
plt.subplot(1,3,2)
#sigma=sigma #0.5
plt.xscale('log')
plt.yscale('log')
plt.xlabel(r'$R=r/10^{%3.2f m}$'%sigma)
plt.ylabel(r'$P(R)=P(r)\times 10^{%3.2f m}$'%sigma)
plt.xlim(1e-5,1e0)
plt.ylim(1e-2,1e3)
xdata = []
ydata = []
y_err = []
for key in X:
# if key > 2:
# continue
xdata += list(X[key]/10**(sigma*np.mean(m_range[key])))
ydata += list(rho_dict[key]*10**(sigma*np.mean(m_range[key])))
y_err += list(Err[key]*10**(sigma*m_mean[key]))
plt.errorbar(X[key]/10**(sigma*m_mean[key]),
rho_dict[key]*10**(sigma*m_mean[key]),
yerr=Err[key]*10**(sigma*m_mean[key]),
label='%2.1f-%2.1f'%(m_range[key][0],m_range[key][1]),
fmt='-o', markersize=8
)
plt.legend(title='m',loc='upper right',bbox_to_anchor=(0.4, .6),fontsize='x-small')
#--- rescaled by r^-\nu
nu = -2.0
plt.subplot(133)
plt.xscale('log')
plt.yscale('log')
plt.xlabel(r'$R$')
plt.ylabel(r'$P(R)\times R^{%3.2f}$'%nu)
#plt.ylabel(r'$\lambda(t) \times t^p$')
plt.xlim(1e-4,1e0)
#plt.ylim(1e-6,1e-4)
KEYS=X.keys()
KEYS.sort()
for key, index in zip(KEYS,xrange(100)):
# if key < 3:
# continue
x_new = X[key]/10**(sigma*m_mean[key])
y_new = rho_dict[key]*10**(sigma*m_mean[key])
y2_new = Err[key]*10**(sigma*m_mean[key])
plt.errorbar(x_new,
y_new/x_new**nu,
yerr=y2_new/x_new**nu,
fmt='-o', markersize=8
)
plt.tight_layout()
###plt.savefig('%s/rho_r.png'%DIR_OUTPT_figs,dpi=75,bbox_inches='tight')
plt.show()
$\rho(r)\propto \frac{r^{\nu_1}}{1+(r/r_c)^{\nu_2}}$¶
In [71]:
from scipy.stats import chi2
#--- fitting
from scipy.optimize import curve_fit
def func(x,a,b1,b2,rc):
return a*x**b1/(1.0+(x/rc)**b2)
sigma=0.5 #kam
pval_max = 0.0
for sigmaa in [sigma]: #np.linspace(0.2,0.5,16):
#--- rescale
x = []
y = []
ye = []
for key in X:
# if key > 1: #kam
# continue
x += list(X[key]/10**(sigmaa*np.mean(m_range[key])))
y += list(rho_dict[key]*10**(sigmaa*np.mean(m_range[key])))
ye += list(Err[key]*10**(sigmaa*m_mean[key]))
#--- initialize
x = np.array(x)
y = np.array(y)
ye=np.array(ye)
#
ss=zip(x,y,ye)
ss.sort()
x=[i[0]for i in ss]
y=[i[1]for i in ss]
ye = [i[2] for i in ss]
#--- fit
popt0, pcov = curve_fit(func, x, y,
p0=(1.0,Df-1,2.0,rc0),sigma=ye) #, bounds=((0.0,0.0), (np.inf,10.0)))
#--- goodness of fit
n=len(x)
m=4 #--- number of coefficients
xsq = np.sum(((y-func(x,*popt0))/ye)**2)
pval=1-chi2.cdf(xsq,n-m)
print pval
if 1: #pval > pval_max:
pval_max = pval
xxdata = x[:]
yydata = y[:]
popt = popt0[:]
sigma = sigmaa
(a,b1,b2,rc)=popt0
nu = -b2
rho_pref = func(rc,a,b1,b2,rc)
#--- plot
fig = plt.figure(figsize=(4,4))
ax=fig.add_subplot(111)
ax.set_xscale('log')
ax.set_yscale('log')
ax.set_xlabel('$r[km]$')
ax.set_ylabel(r'$\rho(r)$')
#ax.set_xlim(2,6)
#ax.set_ylim(1e-4,1e2)
ax.scatter(xxdata,yydata)
# #--- fit
ax.plot(xxdata,func(xxdata,*popt),
'-.r',zorder=3,
label=r'$\rho(r)\propto \frac{r^{%3.2f}}{1+(r/r_c)^{%3.2f}},r_c={%2.1e}$'%(b1,b2,rc))
ax.legend(fontsize='xx-small',frameon=False)
ax.set_title(r'$q=%d,df=%s,\sigma=%3.2f,p=%3.2e$'%(quantile*100,Df,sigma,pval_max),fontsize='xx-small')
#plt.savefig('%s/fit.png'%DIR_OUTPT_figs,dpi=150,bbox_inches='tight',transparent=True)
plt.show()
np.save('%s/nu'%DIR_OUTPT_figs,nu+b1)
np.save('%s/sigma_max'%DIR_OUTPT_figs,sigma)
np.save('%s/pval'%DIR_OUTPT_figs,pval_max)
different realizations¶
In [72]:
alpha_arr=[]
PVAL = []
SIGMA = []
for irun in xrange(16):
a=np.load('runFillmore/Run%s/nu.npy'%(irun))
b=np.load('runFillmore/Run%s/pval.npy'%(irun))
c=np.load('runFillmore/Run%s/sigma_max.npy'%(irun))
# print b.item()
if b.item() < 0.001: #--- remove p < 0.001
continue
alpha_arr.append(a.item())
if irun == 13: print a.item()
PVAL.append([b.item(),irun])
SIGMA.append(c.item())
df=pd.DataFrame({'mean':[np.mean(alpha_arr),np.mean(SIGMA)],
'std_dev':[np.std(alpha_arr),np.std(SIGMA)],
'std_err':[np.std(alpha_arr)/len(alpha_arr)**.5,np.std(SIGMA)/len(SIGMA)**.5]},
index=[r'$\nu$',r'$\sigma$'])
display(df)
print r'%2.1f<\nu<%2.1f'%((df['mean']+2*df['std_dev']).iloc[0],(df['mean']-2*df['std_dev']).iloc[0])
In [73]:
PVAL.sort(reverse=True)
PVAL
Out[73]:
In [74]:
#--- density plots: rho(r) (paper version)
import matplotlib as mpl
mpl.rcParams.update(mpl.rcParamsDefault)
import matplotlib.ticker
from matplotlib import rc as rcc
rcc('text', usetex=True)
font = {'size' : 20}
matplotlib.rc('font', **font)
def returnCMtoInch(x,y):
return (x/2.54,y/2.54)
fig, ax = plt.subplots(figsize=(4,4))
#sigma=0.3 #alpha
xdata = []
ydata = []
colors = ['black','red','green','blue','cyan','brown','violet','magenta','orange','yellow']
fillstyles=['white',None,'white',None,'white',None,'white',None,'white',None,'white',None,'white',None,'white',None]
markers=['o','s','D','^','<','>','v']
assert len(colors) >= len(X)
for key,col,mk,fl in zip(X,colors,markers,fillstyles):
xdata += list(X[key]/10**(sigma*np.mean(m_range[key])))
ydata += list(rho_dict[key]*10**(sigma*np.mean(m_range[key])))
xlabel = '%2.1f-%2.1f'%(m_range[key][0],m_range[key][1])
if key >= 4:
xlabel = '%2.1f'%(m_mean[key])
ax.errorbar(X[key]/10**(sigma*m_mean[key]),
rho_dict[key]*10**(sigma*m_mean[key]),
yerr=Err[key]*10**(sigma*m_mean[key]),
# label=xlabel,
fmt='-o', markersize=8,color=col,marker=mk,markerfacecolor=fl,markeredgewidth=0.7,
linewidth=.5,
barsabove=None,capsize=5,capthick=1,elinewidth=1
)
#(ylo,yhi)=(10**np.floor(np.log10(np.min(ydata))),\
# 10**np.ceil(np.log10(np.max(ydata))))
(ylo,yhi)=(np.min(ydata),\
np.max(ydata))
yhi*=2
ylo/=2
xc=(np.min(xdata)*np.max(xdata))**.5
xlo = xc/(yhi/ylo)**.5
xhi = xc*(yhi/ylo)**.5
ax.axis([xlo,xhi,ylo,yhi])
ax.loglog()
#--- add major xticks
xmin=np.ceil(np.log10(ax.axis()[0]))
xmax=np.floor(np.log10(ax.axis()[1]))
nbin = xmax - xmin
ax.set_xticks(np.logspace(xmin,xmax,int(nbin)+1))
#--- put minor bins
locmin = matplotlib.ticker.LogLocator(base=10.0,subs=(0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1),numticks=12)
ax.xaxis.set_minor_locator(locmin)
ax.xaxis.set_minor_formatter(matplotlib.ticker.NullFormatter())
#plt.xlabel(r'$R=r/10^{%s m}$'%alpha)
#plt.ylabel(r'$P(R)=P(r)\times 10^{%s m}$'%alpha)
#fig.legend(title='m',prop=fontP,loc='upper right',frameon=False)#, bbox_to_anchor=(0.4, .6))
ax.tick_params(axis='y',left=True, right=True,which='both')
ax.tick_params(axis='x',bottom=True, top=True,which='both')
#--- plot power-law
(xlo,xhi)=(rc,100*rc)
yhi=rho_pref/10**.5
ax.plot([xlo,xhi],[yhi, yhi* (xhi/xlo)**(nu+b1)],'r-.',
# label=r'$\rho(r)\propto r^{%3.2f},r_{rup}\propto 10^{%3.2f m}$'%(nu+b1,sigma),
linewidth=1)
#--- rescaled
#ax.scatter(xdata,1e2*np.array(ydata)/np.array(xdata)**(nu+b1))
#ax.legend(fontsize='x-small',frameon=False,bbox_to_anchor=(2.0,1))
ax.set_xlabel(r'$r/r_{rup}$')
ax.set_title(r'$\rho(r)\propto r^{%3.2f},r_{rup}\propto 10^{%3.2f m}$'%(nu+b1,sigma),fontsize='x-small')
#ax.set_title('$q=%d,d_f=%s$'%(quantile*100,Df),fontsize='xx-small')
#ax.set_ylabel(r'$\rho(r)\times r_{rup}$')
#ax.set_title(r'$q=%d,df=%s,p=%3.2e$'%(quantile*100,Df,pval_max),fontsize='xx-small')
#DrawFrame(ax, (0.22,0.06),(0.14,0.06),0.1,LOG_X=True,LOG_Y=True)
#plt.tight_layout()
plt.savefig('%s/rho_rescaled.4.png'%DIR_OUTPT_figs,dpi=75,bbox_inches='tight')
plt.show()
different realizations¶
In [75]:
from IPython.display import Image
for irun in xrange(16):
path = 'runFillmore/Run%s'%irun
#--- load image
display(Image(filename='%s/rho_rescaled.png'%path))
In [76]:
#--- density plots: rho(r) (paper version)
from matplotlib import rc as rcc
import matplotlib as mpl
import matplotlib.ticker
mpl.rcParams.update(mpl.rcParamsDefault)
rcc('text', usetex=True)
font = {'size' : 20}
matplotlib.rc('font', **font)
def returnCMtoInch(x,y):
return (x/2.54,y/2.54)
fig, ax = plt.subplots(figsize=(4,4))
#sigma=alpha
xdata = []
ydata = []
y_err = []
colors = ['black','red','green','blue','cyan','brown','grey','magenta','orange','yellow']
fillstyles=['white',None,'white',None,'white',None,'white',None,'white',None,'white',None,'white',None,'white',None]
markers=['o','s','D','^','<','>','v']
assert len(colors) >= len(X)
for key,col,mk,fl in zip(X,colors,markers,fillstyles):
xdata += list(X[key]/10**(sigma*np.mean(m_range[key])))
ydata += list(rho_dict[key]*10**(sigma*np.mean(m_range[key])))
y_err += list(Err[key]*10**(sigma*m_mean[key]))
ax.errorbar(X[key]/10**(sigma*m_mean[key]),
rho_dict[key]*10**(sigma*m_mean[key]),
yerr=Err[key]*10**(sigma*m_mean[key]),
# label='%2.1f-%2.1f'%(m_range[key][0],m_range[key][1]),
fmt='-o', markersize=8,color=col,marker=mk,markerfacecolor=fl,markeredgewidth=0.7,
linewidth=.5,
barsabove=None,capsize=5,capthick=1,elinewidth=1
)
xdata=np.array(xdata)
ydata=np.array(ydata)
y_err=np.array(y_err)
(ylo,yhi)=(10**np.floor(np.log10(np.min(ydata-y_err))),\
# 10**np.ceil(np.log10(np.max(ydata))))
np.max(ydata))
#(xlo,xhi)=(10**np.floor(np.log10(np.min(xdata))),\
# 10**np.ceil(np.log10(np.max(xdata))))
xc=(np.min(xdata)*np.max(xdata))**.5
xlo = xc/(yhi/ylo)**.5
xhi = xc*(yhi/ylo)**.5
ax.axis([xlo,xhi,ylo,yhi])
ax.loglog()
#--- add major xticks
xmin=np.ceil(np.log10(ax.axis()[0]))
xmax=np.floor(np.log10(ax.axis()[1])) #-1
nbin = xmax - xmin
ax.set_xticks(np.logspace(xmin,xmax,int(nbin)+1))
#--- put minor bins
locmin = matplotlib.ticker.LogLocator(base=10.0,subs=(0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1),numticks=12)
ax.xaxis.set_minor_locator(locmin)
ax.xaxis.set_minor_formatter(matplotlib.ticker.NullFormatter())
#plt.xlabel(r'$R=r/10^{%s m}$'%alpha)
#plt.ylabel(r'$P(R)=P(r)\times 10^{%s m}$'%alpha)
#fig.legend(title='m',prop=fontP,loc='upper right',frameon=False)#, bbox_to_anchor=(0.4, .6))
ax.tick_params(axis='y',left=True, right=True,which='both')
ax.tick_params(axis='x',bottom=True, top=True,which='both')
#--- plot power-law
(xlo,xhi)=(rc,100*rc)
yhi=rho_pref/10**.5
ax.plot([xlo,xhi],[yhi, yhi* (xhi/xlo)**(nu+b1)],'r-.',
# label=r'$\rho(r)\propto r^{%3.2f},r_{rup}\propto 10^{%3.2f m}$'%(nu+b1,sigma),
linewidth=1)
#ax.legend(fontsize='x-small',frameon=False)
#ax.set_xlabel(r'$r/r_{rup}$')
#ax.set_ylabel(r'$\rho(r)\times r_{rup}$')
#ax.set_title('q=%d%%,df=%s'%(quantile*100,Df),fontsize='xx-small')
DrawFrame(ax, (0.22,0.06),(0.14,0.06),0.1,LOG_X=True,LOG_Y=True)
#plt.tight_layout()
plt.savefig('%s/rho_r_2nd.png'%DIR_OUTPT_figs,dpi=300,bbox_inches='tight')
plt.show()
In [77]:
#--- density plots: rho(r) (paper version 2nd)
def returnCMtoInch(x,y):
return (x/2.54,y/2.54)
fig, ax = plt.subplots(figsize=(4,4))
#---
ax.spines['right'].set_visible(False) #--- half open
ax.spines['top'].set_visible(False)
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
#---
#ax.axis([1e-3,1e2,1e-4,1e1])
ax.loglog()
#ax.set_xticks(np.logspace(-1,3,4))
#plt.xlabel(r'$R=r/10^{%s m}$'%alpha)
#plt.ylabel(r'$P(R)=P(r)\times 10^{%s m}$'%alpha)
#plt.xlim(1e-5,1e0)
#plt.ylim(1e-5,1e0)
#colors = ['black','red','green','blue','cyan','brown']
#fillstyles=['white',None,'white',None,'white',None,'white']
#markers=['o','s','D','^','<','v']
#assert len(colors) >= len(X)
xmin = ymin = sys.maxint
ymax=xmax=-sys.maxint
for key,col,mk,fl in zip(X,colors,markers,fillstyles):
if np.max(X[key]) > xmax:
xmax = np.max(X[key])
if np.min(rho_dict[key]) < ymin:
ymin = np.min(rho_dict[key])
if np.max(rho_dict[key]) > ymax:
ymax = np.max(rho_dict[key])
ax.errorbar(X[key],
rho_dict[key],
yerr=Err[key],
label='%2.1f-%2.1f'%(m_range[key][0],m_range[key][1]),
fmt='-o', markersize=8,color=col,marker=mk,markerfacecolor=fl,markeredgewidth=0.7,
linewidth=.5,
barsabove=None,capsize=5,capthick=1,elinewidth=1
)
(ylo,yhi)=(10**np.floor(np.log10(ymin)),\
10**np.ceil(np.log10(ymax)))
xhi=10**np.ceil(np.log10(xmax))
ax.axis([xhi/(yhi/ylo),xhi,ylo,yhi])
#--- add major xticks
xmin=np.ceil(np.log10(ax.axis()[0]))
xmax=np.floor(np.log10(ax.axis()[1]))
nbin = xmax - xmin
ax.set_xticks(np.logspace(xmin,xmax,int(nbin)+1))
#--- put minor bins
locmin = matplotlib.ticker.LogLocator(base=10.0,subs=(0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1),numticks=12)
ax.xaxis.set_minor_locator(locmin)
ax.xaxis.set_minor_formatter(matplotlib.ticker.NullFormatter())
#fig.legend(title='m',prop=fontP,loc='lower left',frameon=False)#, bbox_to_anchor=(0.4, .6))
#ax.tick_params(axis='y',left=True, right=True,which='both')
#ax.tick_params(axis='x',bottom=True, top=True,which='both')
DrawFrame(ax, (0.22,0.06),(0.14,0.06),0.01,LOG_X=True,LOG_Y=True)
#plt.tight_layout()
plt.savefig('%s/rho_r.png'%DIR_OUTPT_figs,dpi=300,bbox_inches='tight',transparent=True)
plt.show()
In [78]:
#--- density plots: rho(r) (paper version 2nd)
#plt.style.use('seaborn')
#plt.rcParams.update({'lines.markeredgewidth': 1})
def returnCMtoInch(x,y):
return (x/2.54,y/2.54)
fig, ax = plt.subplots(figsize=(4,4))
#---
ax.spines['right'].set_visible(False) #--- half open
ax.spines['top'].set_visible(False)
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
#---
ax.axis([40/(20/5e-4),40,5e-4,20])
ax.loglog()
#ax.set_xticks(np.logspace(-1,3,4))
#--- add major xticks
xmin=np.ceil(np.log10(ax.axis()[0]))
xmax=np.floor(np.log10(ax.axis()[1]))
nbin = xmax - xmin
ax.set_xticks(np.logspace(xmin,xmax,int(nbin)+1))
#--- put minor bins
locmin = matplotlib.ticker.LogLocator(base=10.0,subs=(0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1),numticks=12)
ax.xaxis.set_minor_locator(locmin)
ax.xaxis.set_minor_formatter(matplotlib.ticker.NullFormatter())
#--- add major yticks
ymin=np.ceil(np.log10(ax.axis()[2]))
ymax=np.floor(np.log10(ax.axis()[3]))
nbin = ymax - ymin
ax.set_yticks(np.logspace(ymin,ymax,int(nbin)+1))
#--- put minor bins
locmin = matplotlib.ticker.LogLocator(base=10.0,subs=(0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1),numticks=12)
ax.yaxis.set_minor_locator(locmin)
ax.yaxis.set_minor_formatter(matplotlib.ticker.NullFormatter())
ax.set_xlabel(r'$r(km)$')
ax.set_ylabel(r'$\rho(r)$')
#plt.xlim(1e-5,1e0)
#plt.ylim(1e-5,1e0)
#colors = ['black','red','green','blue','cyan','brown']
#fillstyles=['white',None,'white',None,'white',None,'white']
#markers=['o','s','D','^','<','v']
#assert len(colors) >= len(X)
for key,col,mk,fl in zip(X,colors,markers,fillstyles):
xlabel = r'$%2.1f-%2.1f$'%(m_range[key][0],m_range[key][1])
if key == 5:
xlabel = r'$6.4$'
if key == 7:
xlabel = r'$7.1$'
# if key ==
ax.errorbar(X[key],
rho_dict[key],
yerr=Err[key],
label=xlabel,
fmt='-o', markersize=8,color=col,marker=mk,markerfacecolor=fl,markeredgewidth=0.7,
linewidth=.5,
barsabove=None,capsize=5,capthick=1,elinewidth=1
)
ax.legend(title=r'$m$',prop=fontP,loc='lower left',frameon=False,
fontsize ='xx-small',markerscale=1,bbox_to_anchor=(1, 0))
nu=-1.4
ax.plot([1e-1,100],[50, 50* (100/1e-1)**nu],'r-.',linewidth=1)
#ax.tick_params(axis='y',left=True, right=True,which='both')
#ax.tick_params(axis='x',bottom=True, top=True,which='both')
DrawFrame(ax, (0.22,0.06),(0.14,0.06),0.1,LOG_X=True,LOG_Y=True)
#plt.tight_layout()
#plt.savefig('%s/rho_r.png'%DIR_OUTPT_figs,dpi=300,bbox_inches='tight',transparent=True)
In [79]:
from scipy.optimize import curve_fit
def func(x,pref, xmean,sigma):
return pref * np.exp(-((x-xmean)/sigma)**2)
fig=plt.figure(figsize=(8,4))
ax=fig.add_subplot(121)
ax.axis([2e-3,2e-3*1e1/1e-3,1e-3,1e1])
ax.set_xscale('log')
ax.set_yscale('log')
ax.set_xlabel('$r$')
ax.set_ylabel('$P(r)$')
r_peak={}
mm_mean={}
#colors = ['black','red','green','blue','cyan','brown']
#assert len(colors) >= len(X)
p0 = (1.0,0.1,.01)
for key, col in zip(X,colors):
try:
# print np.mean(X[key])
ax.errorbar(X[key],rho_dict[key],
yerr=Err[key],
linestyle='None', color=col,
fmt='-o', markersize=8
)
popt, pcov = curve_fit(func, X[key], rho_dict[key],
sigma=Err[key],
p0=p0) #, bounds=((0.0,0.0), (np.inf,10.0)))
mm_mean[key]=m_mean[key]
p0 = popt[:]
# print p0
r_peak[key] = popt[1]
# if key == 5:
ax.plot(X[key], func(X[key], *popt),'-',color=col)#,label='fit: r=%3.2f' % (popt[1]))
ax.legend()
except:
continue
ax=fig.add_subplot(122)
ax.set_yscale('log')
ax.set_xlabel('$m$')
ax.set_ylabel('$r$')
#ax.set_ylim(1,1e3)
ax.plot(mm_mean.values(),r_peak.values(),'o')
#
#
def func(x,c,alpha):
return c*10**(alpha*x)
#
popt, pconv = curve_fit( func, mm_mean.values(),r_peak.values() )
#
ax.plot(mm_mean.values(),func( np.array(mm_mean.values()),*popt),'--r')
print popt
print pconv**0.5
fig.tight_layout()
In [80]:
#--- fitting
from scipy.optimize import curve_fit
def func(x,a,b):
return a/x**b
xdata = np.array(xdata)
xxdata = xdata[xdata>2e-2]
ydata = np.array(ydata)
yydata = ydata[xdata>2e-2]
popt, pcov = curve_fit(func, xxdata, yydata, p0=(1.0,1.0), bounds=((0.0,0.0), (np.inf,10.0)))
plt.figure(figsize=(5,5))
plt.xscale('log')
plt.yscale('log')
#plt.xlim(1e-1,1e2)
#plt.ylim(1e-4,1e-1)
plt.plot(xdata, ydata,marker='o',linestyle='None')
plt.plot(xdata, func(xdata, *popt),'r-',label='fit: a=%3.2f' % popt[1])
plt.legend()
#plt.plot(xdata, func(xdata, *popt), 'g--',
# label='fit: a=%5.3f, b=%5.3f' % tuple(popt))
In [81]:
#--- choose bins for rho and lambda
import traceback
#--------------------
#----- subset (the same as trig. analysis)
#--------------------
swarm_lohi = DataFrameSubSet( swarm, #--- complete catalog
'magnitude',
( mc, sys.maxint ) )
swarm_lohi.reset_index(inplace=True,drop=True)
#--- remove pairs with r > cs.t
#cs = 3 * (24*3600) #--- km per day
df_trig = nij_trig.copy()
#--- parents' magnitudes
m_list = GetParentsMagnitudes( swarm_lohi, df_trig )
#--- number of daughters for each mother
df_nn = df_trig.groupby(by='Parent_id').count()['Event_id']
#--- include daughters with zero children
list_of_zero_afs = set(df_trig['Event_id'])-set(df_trig['Parent_id'])
df_zeros = pd.Series(np.zeros(len(list_of_zero_afs)),index=list_of_zero_afs)
#--- scattered plot
fig = plt.figure(figsize=(4,4),frameon=True)
ax = fig.add_subplot(111)
#ax.set_xlim(mc,swarm_lohi['magnitude'].max()+0.5)
m_min = min(m_list)-1.0e-6
m_max = max(m_list)+1.0e-6 #--- exclude the largest event
ax.set_xlim(m_min,np.ceil(m_max))
ax.set_ylim(0.1,1000)
ax.plot( swarm_lohi['magnitude'].loc[df_nn.index],
df_nn,
'o',color='black',alpha=.1)
ax.plot( swarm_lohi['magnitude'].loc[df_zeros.index],
df_zeros,
'x',color='gray')
plt.yscale('log')
#plt.xlabel('$m$')
#plt.ylabel(r'$N_{as}$')
#--- choose m0<m<m1
dm = 0.75 #0.5
n = int( (6.0 - m_min ) / dm )
m = list(np.linspace(m_min,6.0,n))
#m=AdjustBins(m_list,m)
# m=[2.7999989999999997,
# 3.133332555555555,
# 3.466666111111111,
# 3.7999996666666664,
# 4.133333222222222,
# 4.466666777777778,
# 4.800000333333333,
# 5.800001]
m+=[6.41,7.1-0.01,7.1+0.01]
Mlist=m
m_mean=np.array(np.zeros(len(m) - 1))
m_err=np.array(np.zeros(len(m) - 1))
N_as = np.array(np.zeros(len(m) - 1))
err_N = np.array(np.zeros(len(m) - 1))
for i in xrange( len(m) - 1 ):
try:
m0 = m[ i ]
m1 = m[ i + 1 ]
df, m_mean[ i ], m_err[i] = GetPairsWithSpecifiedParentMag((m0,m1),
swarm_lohi,df_trig) #--- get parent with m0<m<m1
df.reset_index( inplace = True, drop = True )
# pdb.set_trace()
#--- number of daughters for each mother
df_n = df.groupby(by='Parent_id').count()['Event_id']
#--- include daughters with zero children
list_of_zero_afs = set(df_trig['Event_id'])-set(df_trig['Parent_id'])
subset = swarm_lohi.loc[list_of_zero_afs]
list_of_zero_afs = subset[(subset['magnitude'] >= m0) & (subset['magnitude'] <= m1)].index
df_zeros = pd.Series(np.zeros(len(list_of_zero_afs)),index=list_of_zero_afs)
#--- mean
# print [m0,m1],list_of_zero_afs
# pdb.set_trace()
N_as[ i ] = 1.0*(df_n.sum()+ df_zeros.sum())/(len(df_n)+len(df_zeros))
err_N[ i ] = (N_as[ i ]/(len(df_n)+len(df_zeros)))**0.5 #--- poisson
# err_N[ i ]=np.std(df_n.tolist()+df_zeros.tolist())/(len(df_n)+len(df_zeros))**0.5
except:
# traceback.print_exc()
continue
#ax.plot(m, np.append(N_as,N_as[-1]), linestyle='-', drawstyle='steps-post',color='red')
ax.errorbar(m_mean,N_as,
yerr=err_N,xerr=m_err,
markerfacecolor='white',
fmt='o', markersize=8,color='red',markeredgewidth=0.7,
linewidth=.5,
barsabove=None,capsize=5,capthick=1,elinewidth=1)
#--- add major xticks
xmin=np.ceil(ax.axis()[0])
xmax=np.floor(ax.axis()[1])
nbin = xmax - xmin
ax.set_xticks(np.linspace(xmin,xmax,int(nbin)+1))
DrawFrame(ax, (0.15,0.08),(0.14,0.06),0.1,LOG_Y=True)
try:
from scipy.optimize import curve_fit
def func(x,c,alpha):
return c*10**(alpha*x)
popt, pconv = curve_fit(func,m_mean[m_mean>=mc],N_as[m_mean>=mc])
mm = swarm_lohi['magnitude'].loc[df_zeros.index].tolist() + \
swarm_lohi['magnitude'].loc[df_nn.index].tolist() #swarm_lohi[swarm_lohi['magnitude']>=mc]['magnitude']
mm = np.array(mm)
mm=list(set(mm))
mm.sort()
mm=np.array(mm)
ax.plot(mm,func(mm,*popt),'-.g')
print popt
print pconv**0.5
except:
pass
#plt.savefig('%s/prod.png'%DIR_OUTPT_figs,dpi=150,bbox_inches='tight')
fig = plt.figure(figsize=(4,4),frameon=True)
ax = fig.add_subplot(111)
ax.plot(m, np.append(N_as,N_as[-1]), linestyle='-', drawstyle='steps-post',color='red')
ax.errorbar(m_mean,N_as,
yerr=err_N,xerr=m_err,
markerfacecolor='white',
fmt='o', markersize=8,color='red',markeredgewidth=0.7,
linewidth=.5,
barsabove=None,capsize=5,capthick=1,elinewidth=1)
ax.set_xlim(m_min,np.ceil(m_max))
ax.set_ylim(0.1,1000)
ax.set_yscale('log')
ax.set_xticks(np.linspace(xmin,xmax,int(nbin)+1))
plt.show()
In [82]:
#--- omori relation
import numpy as np
import math
from scipy.optimize import curve_fit
#def func(x,c,p,A):#,B):
# return A/(1+x/c)**p
def func(x,c,p,A,c2,p2):#,B):
return A/(1+(x/c)**p+(x/c2)**p2)
#def func(x,c,p):#,B):
# return (p-1)/c/(1+x/c)**p
#--------------------
#----- subset (the same as trig. analysis)
#--------------------
swarm_lohi = DataFrameSubSet( swarm, #--- complete catalog
'magnitude',
( mc, sys.maxint ) )
swarm_lohi.reset_index(inplace=True,drop=True)
popt={}
pcov={}
perr = {}
##--- parents' magnitudes
#m_list = GetParentsMagnitudes( swarm_lohi, df_trig )
#m_min = min(m_list)-1.0e-6
#m_max = max(m_list)+1.0e-6 #--- exclude the largest event
#
##--- choose m0<m<m1
#dm = 0.3
#n = int( ( m_max - m_min ) / dm )
#m = list(np.linspace(m_min,m_max,n))
#m=AdjustBins(m_list,m)
#Mlist=m
X={}
rho_dict={}
#m_range={}
Err={}
m_mean=np.array(np.zeros(len(m)-1))
Xedges={}
nrows=len(m)-1;ncols=2
fig=plt.figure(figsize=(ncols*4,nrows*4))
for i in xrange( len(m) - 1 ):
# if i == (len(m) - 2):
# pdb.set_trace()
try:
m0 = m[ i ]
m1 = m[ i + 1 ]
print (m0,m1)
df_trig,m_mean[ i ],junk = GetPairsWithSpecifiedParentMag((m0,m1),swarm_lohi,nij_trig) #--- get parent with m0<m<m1
df_trig.reset_index( inplace = True, drop = True )
# print "# of mother events:%s"%len(df_trig.groupby(by="Parent_id"))
#--- number of daughters for each mother
df_n = df_trig.groupby(by='Parent_id').count()['Event_id']
#--- include daughters with zero children
list_of_zero_afs = set(df_trig['Event_id'])-set(df_trig['Parent_id'])
subset = swarm_lohi.loc[list_of_zero_afs]
list_of_zero_afs = subset[(subset['magnitude'] >= m0) & (subset['magnitude'] <= m1)].index
df_zeros = pd.Series(np.zeros(len(list_of_zero_afs)),index=list_of_zero_afs)
#--- mean
N_as = 1.0*(df_n.sum()+ df_zeros.sum())/(len(df_n)+len(df_zeros))
# print 'N_as=%s'%N_as
#--- add distance & time column
# df_trig['R'] = rmat[df_trig['Parent_id'],df_trig['Event_id']]
# df_trig['T'] = tmat[df_trig['Parent_id'],df_trig['Event_id']]
# assert len ( df_trig[ df_trig['R'] == 0.0 ] ) == 0, '%s'%display( df_trig[ df_trig['R'] == 0.0 ] )
#--- remove pairs with r > cs.t
# cs = 3 * (24*3600) #--- km per day
# df_trig = RemovePair( df_trig, cs )
#--- rho plots
n_decades = int( math.ceil( log(df_trig['T'].max()/df_trig['T'].min(),10) ) )
nbin_per_decade = 4
nbins = nbin_per_decade * n_decades
bins = np.logspace(log(df_trig['T'].min(),10)-1.e-10,
log(df_trig['T'].max(),10)+1.e-10,nbins)
bins = AdjustBins(df_trig['T'],bins)
rho, xedges=np.histogram(df_trig['T'], #--- density
density=True,
bins=bins)
rho *= N_as #--- int rho = N_as
hist, xedges=np.histogram(df_trig['T'], #--- histogram
bins=bins)
x_bins, junk=np.histogram(df_trig['T'], #--- histogram
bins=bins,
weights = df_trig['T'])
#--- rm empty bins
x_bins = x_bins[ hist != 0 ]
rho = rho[ hist != 0 ]
hist = hist[ hist != 0 ]
#--- poisson err
err = rho/np.sqrt(hist)
x_bins /= hist
#---- fit
# fit = plfit.plfit( np.array(df_trig['T']) ) #--- clauset
# cval = fit[1] #--- completeness mag.
# pval = fit[0]
# [pval, gof] = plpva.plpva(np.array(df_trig['T']), cval, 'xmin', cval,'silent')
# print pval
#--- 2nd fit
try:
popt[i], pcov[i] = curve_fit(func, x_bins, rho,
p0=(1.0e-3,1.5,1e3,1e0,2.0),
bounds=((1.0e-6,0.1,1e-5,1e-6,0.1), (np.inf,7,np.inf,np.inf,7)), #c,p,A,c2,p2
sigma=err #rho**0.5 #err
# absolute_sigma = True,
# method='trf'#'dogbox'
)
perr[i] = np.sqrt(np.diag(pcov[i]))
except:
pass
#--- scattered plot
ax=fig.add_subplot(nrows,ncols,2*i+1)
ax.set_title(r'$%2.1f<m<%2.1f$'%(m0,m1))
ax.set_xscale('log')
ax.set_yscale('log')
ax.set_xlabel('$t$')
ax.set_ylabel('$r$')
#plt.xlim(1e-3,100)
#plt.ylim(1e-3,1e2)
ax.scatter(df_trig['T'],df_trig['R'],alpha=0.1)
#--- discretization effects
dt_min=df_trig['T'].min()
dt_max=df_trig['T'].max()
dr_min=df_trig['R'].min()
dr_max=df_trig['R'].max()
ax.plot([dt_min,dt_min],[dr_min,dr_max],
'-',color='blue')
ax.plot([dt_max,dt_max],[dr_min,dr_max],
'-',color='blue')
ax.plot([dt_min,dt_max],[dr_min,dr_min],
'-',color='blue')
ax.plot([dt_min,dt_max],[dr_max,dr_max],
'-',color='blue')
ax.set_ylim(dr_min/2,dr_max*2)
ax.plot([dt_min,dt_max],[dt_min*cs,dt_max*cs],
'-',color='red')
#--- rho
ax=fig.add_subplot(nrows,ncols,2*i+2)
ax.set_xlim(1e-4,1e2)
# ax.set_ylim(1e-3,1e3)
ax.set_xscale('log')
ax.set_yscale('log')
ax.set_xlabel('$t$')
ax.set_ylabel('$\lambda(t)$')
ax.errorbar(x_bins,rho,
yerr=err,
linestyle='None',
fmt='-o', markersize=8
)
#--- plot the fit
# plt.plot(x_bins,
# (pval-1)/cval/(1+x_bins/cval)**pval,
# label='fit: p=%2.1f, c=%4.3f' % (pval,cval)
# )
#--- 2nd fit
try:
ax.plot(x_bins, func(x_bins, *popt[i]),'r-',label='fit: p0=%3.2f, p1=%3.2f' % (popt[i][1],popt[i][4]))
except:
traceback.print_exc()
pass
fig.tight_layout()
ax.legend(fontsize='x-small') #prop=fontP)#bbox_to_anchor=(1.5, 0.5))
X[i] = x_bins[:]
Xedges[i]=xedges
rho_dict[i]=rho[:]
# m_range[i]=np.array([m0,m1])
Err[i]=err[:]
except:
continue
#fig.savefig('%s/rho_t.png'%DIR_OUTPT_figs,dpi=75,bbox_inches='tight')
plt.show()
In [83]:
KEYS=popt.keys()
KEYS.sort()
M_Mean=[]
pval=[]
cval = []
cerr = []
aval = []
aerr = []
mm=[]
pperr=[]
AVAL = {}
fig = plt.figure(figsize=(12,4))
ax=fig.add_subplot(131)
for ikey in KEYS: #--- exclude the last point
pval.append( min(popt[ikey][1],popt[ikey][4]) )
cval.append( min(popt[ikey][0],popt[ikey][3]) )
aval.append( popt[ikey][2] )
AVAL[ikey]=popt[ikey][2]
aerr.append(perr[ikey][2])
index = min([popt[ikey][1],1],[popt[ikey][4],4])[1]
pperr.append(perr[ikey][index])
cerr.append(perr[ikey][index-1])
M_Mean.append(m_mean[ikey])
ax.errorbar(M_Mean,pval,yerr=pperr,
marker='o',color='black')
#ax.set_xlim(0,4)
ax.set_ylim(0,3)
ax.set_xlabel('$m$')
ax.set_ylabel('$p$')
ax.set_title('nth=%2.1e'%n_thresh)
#ax.plot([0,3],[1.29,1.29],'--r')
#ax.plot([0,3],[1.37,1.37],'--r')
#--- plot c
def func(x,a,b):
return a*10**(x*b)
poptt, pcovv = curve_fit(func, M_Mean,cval, sigma=cerr)
print poptt
ax2=fig.add_subplot(132)
ax2.set_ylim(1e-4,1e-1)
#ax2.set_xlim(0,4)
ax2.set_yscale('log')
ax2.set_ylabel('$c$')
ax2.set_xlabel('$m$')
ax2.errorbar(M_Mean,cval,yerr=cerr,
marker='o',color='black')
try:
ax2.plot(M_Mean,func(M_Mean,*poptt),'--r')
#--- plot A
poptt, pcovv = curve_fit(func, M_Mean,aval, sigma=aerr)
ax3=fig.add_subplot(133)
#ax3.set_ylim(1e2,1e4)
#ax3.set_xlim(0,4)
ax3.set_yscale('log')
ax3.set_ylabel('$A$')
ax3.set_xlabel('$m$')
ax3.errorbar(M_Mean,aval,yerr=aerr,
marker='o',color='black')
ax3.plot(m_mean,func(M_Mean,*poptt),'--r')
print poptt
except:
pass
fig.tight_layout()
#plt.savefig('%s/p.png'%DIR_OUTPT_figs,dpi=75,bbox_inches='tight')
plt.show()
In [84]:
#--- omori relation
plt.figure(figsize=(16.5,5))
#--- unrescaled
plt.subplot(131)
plt.xscale('log')
plt.yscale('log')
plt.xlabel('$t$')
plt.ylabel('$\lambda(t)$')
#plt.xlim(1e-6,1e1)
#plt.ylim(1e0,1e7)
KEYS = X.keys()
KEYS.sort()
for key, index in zip(KEYS,xrange(100)):
plt.errorbar(X[key],rho_dict[key],yerr=Err[key],
# label='%2.1f-%2.1f'%(m_range[key][0],m_range[key][1]),
fmt='-o', markersize=8
)
#plt.legend(title='m',fontsize='small',loc='upper right',bbox_to_anchor=(0.4, .65),frameon=False)
xdata = []
ydata = []
y_err = []
#--- rescaled
alpha_c = 0.0 #0.5
#alpha_p = 0.43 #--- productivity
alpha_y = alpha_c - alpha_p
plt.subplot(132)
plt.xscale('log')
plt.yscale('log')
plt.xlabel(r'$t/10^{%3.2f\times m}$'%alpha_c)
plt.ylabel(r'$\lambda(t) \times 10^{(%3.2f-%3.2f)m}$'%(alpha_c,alpha_p))
#plt.ylabel(r'$\lambda(t) \times t^p$')
#plt.xlim(1e-6,1e0)
#plt.ylim(1e-3,1e5)
aval=AVAL
for key, index in zip(KEYS,xrange(100)):
try:
# xdata += list(X[key]/10**(alpha_c*m_mean[key]))
# print key, aval[key]
xdata += list(X[key]/aval[key])
# ydata += list(rho_dict[key]*10**(alpha_y*m_mean[key]))
ydata += list(rho_dict[key]*aval[key]*10**(alpha_y*m_mean[key]))
# y_err += list(Err[key]*10**(alpha_y*m_mean[key]))
y_err += list(Err[key]*aval[key]*10**(alpha_y*m_mean[key]))
# plt.errorbar(X[key]/10**(alpha_c*m_mean[key]),
# rho_dict[key]*10**(alpha_y*m_mean[key]),
# yerr=Err[key]*10**(alpha_y*m_mean[key]),
# # label='%2.1f-%2.1f'%(m_range[key][0],m_range[key][1]),
# label='%2.1f'%(m_mean[key]),
# fmt='-o', markersize=8
#
plt.errorbar(X[key]/aval[key],
rho_dict[key]*aval[key]*10**(alpha_y*m_mean[key]),
yerr=Err[key]*aval[key]*10**(alpha_y*m_mean[key]),
# label='%2.1f-%2.1f'%(m_range[key][0],m_range[key][1]),
label='%2.1f'%(m_mean[key]),
fmt='-o', markersize=8
)
plt.legend(title='m',fontsize='small',loc='upper right',bbox_to_anchor=(0.4, .65),frameon=False)
except:
continue
#--- rescaled by t^-p
p = 1
plt.subplot(133)
plt.xscale('log')
plt.yscale('log')
plt.xlabel(r'$t/10^{%3.2f\times m}$'%alpha_c)
plt.ylabel(r'$\lambda(t) \times 10^{(%3.2f-%3.2f)m} \times t^{%3.2f}$'%(alpha_c,alpha_p,p))
#plt.ylabel(r'$\lambda(t) \times t^p$')
#plt.xlim(1e-6,1e0)
#plt.ylim(1e-5,1e-3)
for key, index in zip(KEYS,xrange(100)):
x_new = X[key]/10**(alpha_c*m_mean[key])
y_new = rho_dict[key]*10**(alpha_y*m_mean[key])
y2_new = Err[key]*10**(alpha_y*m_mean[key])
plt.errorbar(x_new,
y_new*x_new**p,
yerr=y2_new*x_new**p,
fmt='-o', markersize=8
)
plt.tight_layout()
##plt.savefig('%s/rho_t_mult.png'%DIR_OUTPT_figs,dpi=75,bbox_inches='tight')
plt.show()
$\rho(t)\propto 1/((t/t_0)^{p_0}+(t/t_1)^{p_1})$¶
In [85]:
#--- fitting
from scipy.optimize import curve_fit
def func(x,c,p,A):
return A/(1+(x/c)**p)
#def func(x,b,a):
# return a*x**b
#tc=1e-3
xdata = np.array(xdata)
xxdata = xdata[:]#[xdata>tc]
ydata = np.array(ydata)
yydata = ydata[:] #xdata>tc]
Y_err=y_err
#
ss=zip(xxdata,yydata,Y_err)
ss.sort()
xxdata=[i[0]for i in ss]
yydata=[i[1]for i in ss]
Y_err = [i[2] for i in ss]
popt, pcov = curve_fit(func, xxdata, yydata,
p0=(1.0e-2,1.0,1e2),#,1e0,2.0),
bounds=((1.0e-6,0.1,1e-5), (np.inf,7,np.inf)), #c,p,A,c2,p2
sigma=Y_err)
p = -popt[1]
rho_pref = func(np.min(xxdata),*popt)
[tlo,thi]=[popt[0],1e10]
#--- goodness of fit
n=len(xxdata)
m=3 #--- number of coefficients
xsq = np.sum(((yydata-func(xxdata,*popt))/Y_err)**2)
pval=1-chi2.cdf(xsq,n-m)
print 'p=',pval
#--- linear
#popt = np.polyfit(np.log10(xxdata),np.log10(yydata), 1)
#popt[1] = 10**(popt[1])
#p = popt[0]
#rho_pref = popt[1]
#--- plot
fig = plt.figure(figsize=(4,4))
ax=fig.add_subplot(111)
ax.set_xscale('log')
ax.set_yscale('log')
ax.set_xlabel('$t$')
ax.set_ylabel(r'$\lambda(t)$')
#ax.set_xlim(2,6)
#ax.set_ylim(1e-4,1e2)
ax.scatter(xdata,ydata)
ax.scatter(xdata,ydata*xdata**(-p))
ax.scatter([popt[0]],func(np.array([popt[0]]),*popt), #--- size
marker='x',c='black',s=100)
#--- fit
ax.plot(xxdata,func(xxdata,*popt),
'-.r',zorder=3,
label=r'$\lambda(t)\propto t^{%3.2f}$'%(p))
ax.legend(fontsize='xx-small',frameon=False)
#ax.set_title('q=%d%%,df=%s'%(quantile*100,Df),fontsize='xx-small')
plt.savefig('%s/omori_1st.png'%DIR_OUTPT_figs,dpi=75,bbox_inches='tight',transparent=True)
#--- save p
np.save('omori_exp1st',p)
plt.show()
linear fit with t>tc¶
In [86]:
#--- linear fitting
from scipy.optimize import curve_fit
def func(x,b,a):
return a*x**b
xdata = np.array(xdata)
xxdata = xdata[np.all([xdata>tlo,xdata<thi],axis=0)]
#
ydata = np.array(ydata)
yydata = ydata[np.all([xdata>tlo,xdata<thi],axis=0)]
#
y_err = np.array(y_err)
Y_err=y_err[np.all([xdata>tlo,xdata<thi],axis=0)]
#
ss=zip(xxdata,yydata,Y_err)
ss.sort()
xxdata=[i[0]for i in ss]
yydata=[i[1]for i in ss]
Y_err = [i[2] for i in ss]
#--- linear
popt = np.polyfit(np.log10(xxdata),np.log10(yydata), 1,
w=np.array(yydata)/np.array(Y_err))
popt[1] = 10**(popt[1])
p = popt[0]
rho_pref = popt[1]
#--- goodness of fit
n=len(xxdata)
m=2 #--- number of coefficients
xsq = np.sum(((yydata-func(xxdata,*popt))/Y_err)**2)
pval=1-chi2.cdf(xsq,n-m)
print 'p=',pval
#--- plot
fig = plt.figure(figsize=(4,4))
ax=fig.add_subplot(111)
ax.set_xscale('log')
ax.set_yscale('log')
ax.set_xlabel('$t$')
ax.set_ylabel(r'$\lambda(t)$')
#ax.set_xlim(2,6)
#ax.set_ylim(1e-4,1e2)
ax.scatter(xdata,ydata)
ax.scatter(xdata,ydata*xdata**(-p))
#ax.scatter([popt[0]],func(np.array([popt[0]]),*popt), #--- size
# marker='x',c='black',s=100)
#--- fit
ax.plot(xxdata,func(xxdata,*popt),
'-.r',zorder=3,
label=r'$\lambda(t)\propto t^{%3.2f}$'%(p))
ax.legend(fontsize='xx-small',frameon=False)
#ax.set_title('q=%d%%,df=%s'%(quantile*100,Df),fontsize='xx-small')
plt.savefig('%s/omori_2nd.png'%DIR_OUTPT_figs,dpi=75,bbox_inches='tight',transparent=True)
#--- save p
np.save('omori_exp2nd',p)
plt.show()
In [87]:
#--- omori (paper version)
#--- rescaled
fig, ax = plt.subplots(figsize=(4,4))
#ax.axis([1/(20/3e-3),1,3e-3,20])
#ax.loglog()
#colors = ['black','red','green','blue','cyan','brown']
#fillstyles=['white',None,'white',None,'white',None,'white']
#markers=['o','s','D','^','<','v']
#assert len(colors) >= len(X)
xdata = []
ydata = []
for key,col,mk,fl in zip(X,colors,markers,fillstyles):
xdata += list(X[key]/10**(alpha_c*m_mean[key]))
ydata += list(rho_dict[key]*10**(alpha_y*m_mean[key]))
ax.errorbar(X[key]/10**(alpha_c*m_mean[key]),
rho_dict[key]*10**(alpha_y*m_mean[key]),
yerr=Err[key]*10**(alpha_y*m_mean[key]),
# label='%2.1f-%2.1f'%(m_range[key][0],m_range[key][1]),
fmt='-o', markersize=8,color=col,marker=mk,markerfacecolor=fl,markeredgewidth=0.7,
linewidth=.5,
barsabove=None,capsize=5,capthick=1,elinewidth=1
)
(ylo,yhi)=(10**np.floor(np.log10(np.min(ydata))),\
10**np.ceil(np.log10(np.max(ydata))))
xhi=10**np.ceil(np.log10(np.max(xdata)))
ax.axis([xhi/(yhi/ylo),xhi,ylo,yhi])
ax.loglog()
##--- add major xticks
xmin=np.ceil(np.log10(ax.axis()[0]))
xmax=np.floor(np.log10(ax.axis()[1]))
nbin = xmax - xmin
ax.set_xticks(np.logspace(xmin,xmax,int(nbin)+1))
#--- add major yticks
ymin=np.ceil(np.log10(ax.axis()[2]))
ymax=np.floor(np.log10(ax.axis()[3]))
nbin = ymax - ymin
ax.set_yticks(np.logspace(ymin,ymax,int(nbin)+1))
#--- put minor bins
locmin = matplotlib.ticker.LogLocator(base=10.0,subs=(0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1),numticks=12)
ax.xaxis.set_minor_locator(locmin)
ax.xaxis.set_minor_formatter(matplotlib.ticker.NullFormatter())
#--- put minor bins y
locmin = matplotlib.ticker.LogLocator(base=10.0,subs=(0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1),numticks=12)
ax.yaxis.set_minor_locator(locmin)
ax.yaxis.set_minor_formatter(matplotlib.ticker.NullFormatter())
#fig.legend(title='m',prop=fontP,loc='upper right',frameon=False)#, bbox_to_anchor=(0.4, .6))
ax.tick_params(axis='y',left=True, right=True,which='both')
ax.tick_params(axis='x',bottom=True, top=True,which='both')
ax.set_xlabel('$t(day)$')
ax.set_ylabel('$\lambda(t)/10^{%3.2fm}$'%alpha_p)
#--- plot power-law
(xlo,xhi)=(10**xmin,10**(xmin+6)) #(0.8*15e-3,0.8*.6)
yhi=func(xlo,*popt)*1e-2 #rho_pref #*xmin**p/10
ax.plot([xlo,xhi],[yhi, yhi* (xhi/xlo)**p],'r-.',
label=r'$\lambda(t)\propto t^{%3.2f}$'%(p),
linewidth=1)
ax.legend(fontsize='x-small',frameon=False)
ax.set_xlabel(r'$t$')
#ax.set_ylabel(r'$\rho(r)\times r_{rup}$')
ax.set_title('q=%d,df=%s'%(quantile*100,Df),fontsize='xx-small')
DrawFrame(ax, (0.22,0.06),(0.14,0.06),0.01,LOG_X=True,LOG_Y=True)
#plt.tight_layout()
plt.savefig('%s/rho_t2nd.png'%DIR_OUTPT_figs,dpi=75,bbox_inches='tight')
plt.show()
In [88]:
#--- omori (paper version)
import re
# create a definition for the short hyphen
matplotlib.rcParams["text.latex.preamble"].append(r'\mathchardef\mhyphen="2D')
class MyLogFormatter(matplotlib.ticker.LogFormatterMathtext):
def __call__(self, x, pos=None):
# call the original LogFormatter
rv = matplotlib.ticker.LogFormatterMathtext.__call__(self, x, pos)
# check if we really use TeX
if matplotlib.rcParams["text.usetex"]:
# if we have the string ^{- there is a negative exponent
# where the minus sign is replaced by the short hyphen
rv = re.sub(r'\^\{-', r'^{\mhyphen', rv)
return rv
#--- rescaled
fig, ax = plt.subplots(figsize=(4,4))
#ax.axis([1/(20/3e-3),1,3e-3,20])
#ax.loglog()
#colors = ['black','red','green','blue','cyan','brown']
#fillstyles=['white',None,'white',None,'white',None,'white']
#markers=['o','s','D','^','<','v']
#assert len(colors) >= len(X)
for key,col,mk,fl in zip(X,colors,markers,fillstyles):
ax.errorbar(X[key]/10**(alpha_c*m_mean[key]),
rho_dict[key]*10**(alpha_y*m_mean[key]),
yerr=Err[key]*10**(alpha_y*m_mean[key]),
# label='%2.1f-%2.1f'%(m_range[key][0],m_range[key][1]),
fmt='-o', markersize=8,color=col,marker=mk,markerfacecolor=fl,markeredgewidth=0.7,
linewidth=.5,
barsabove=None,capsize=5,capthick=1,elinewidth=1
)
(ylo,yhi)=(10**np.floor(np.log10(np.min(ydata))),\
# 10**np.ceil(np.log10(np.max(ydata))))
np.max(ydata))
#(xlo,xhi)=(10**np.floor(np.log10(np.min(xdata))),\
# 10**np.ceil(np.log10(np.max(xdata))))
xc=(np.min(xdata)*np.max(xdata))**.5
xlo = xc/(yhi/ylo)**.5
xhi = xc*(yhi/ylo)**.5
ax.axis([xlo,xhi,ylo,yhi])
ax.loglog()
##--- add major xticks
xmin=np.ceil(np.log10(ax.axis()[0]))
xmax=np.floor(np.log10(ax.axis()[1]))
nbin = xmax - xmin
ax.set_xticks(np.logspace(xmin,xmax,int(nbin)+1))
#--- add major yticks
ymin=np.ceil(np.log10(ax.axis()[2]))
ymax=np.floor(np.log10(ax.axis()[3]))
nbin = ymax - ymin
ax.set_yticks(np.logspace(ymin,ymax,int(nbin)+1))
#--- put minor bins
locmin = matplotlib.ticker.LogLocator(base=10.0,subs=(0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1),numticks=12)
ax.xaxis.set_minor_locator(locmin)
ax.xaxis.set_minor_formatter(matplotlib.ticker.NullFormatter())
ax.xaxis.set_major_formatter(MyLogFormatter()) #--- minus sign too long
#--- put minor bins y
locmin = matplotlib.ticker.LogLocator(base=10.0,subs=(0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1),numticks=12)
ax.yaxis.set_minor_locator(locmin)
ax.yaxis.set_minor_formatter(matplotlib.ticker.NullFormatter())
ax.xaxis.set_major_formatter(MyLogFormatter()) #--- minus sign too long
#fig.legend(title='m',prop=fontP,loc='upper right',frameon=False)#, bbox_to_anchor=(0.4, .6))
ax.tick_params(axis='y',left=True, right=True,which='both')
ax.tick_params(axis='x',bottom=True, top=True,which='both')
#ax.set_xlabel('$t(day)$')
#ax.set_ylabel('$\lambda(t)/10^{%3.2fm}$'%alpha_p)
#--- plot power-law
tc=tlo
(xlo,xhi)=(tc,1e6*tc) #(0.8*15e-3,0.8*.6)
yhi=rho_pref*tc**p*10
ax.plot([xlo,xhi],[yhi, yhi* (xhi/xlo)**p],'r-.',
# label=r'$\lambda(t)\propto t^{%3.2f}$'%(p),
linewidth=1)
#ax.legend(fontsize='x-small',frameon=False)
#ax.set_xlabel(r'$t$')
#ax.set_ylabel(r'$\rho(r)\times r_{rup}$')
#ax.set_title('q=%d%%,df=%s'%(quantile*100,Df),fontsize='xx-small')
DrawFrame(ax, (0.22,0.06),(0.14,0.06),0.1,LOG_X=True,LOG_Y=True)
#plt.tight_layout()
#plt.savefig('%s/rho_t2nd.png'%DIR_OUTPT_figs,dpi=300,bbox_inches='tight')
plt.show()
In [89]:
#--- density plots: rho(r) (paper version 2nd)
#plt.style.use('seaborn')
#plt.rcParams.update({'lines.markeredgewidth': 1})
def returnCMtoInch(x,y):
return (x/2.54,y/2.54)
fig, ax = plt.subplots(figsize=(4,4))
#---
ax.spines['right'].set_visible(False) #--- half open
ax.spines['top'].set_visible(False)
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
#---
#ax.axis([1e-3,1e2,1e-4,1e1])
ax.loglog()
#ax.set_xticks(np.logspace(-1,3,4))
#plt.xlabel(r'$R=r/10^{%s m}$'%alpha)
#plt.ylabel(r'$P(R)=P(r)\times 10^{%s m}$'%alpha)
#plt.xlim(1e-5,1e0)
#plt.ylim(1e-5,1e0)
#colors = ['black','red','green','blue','cyan','brown']
#fillstyles=['white',None,'white',None,'white',None,'white']
#markers=['o','s','D','^','<','v']
#assert len(colors) >= len(X)
xmin = ymin = sys.maxint
ymax=xmax=-sys.maxint
for key,col,mk,fl in zip(X,colors,markers,fillstyles):
if np.max(X[key]) > xmax:
xmax = np.max(X[key])
if np.min(X[key]) < xmin:
xmin = np.min(X[key])
if np.min(rho_dict[key]) < ymin:
ymin = np.min(rho_dict[key])
if np.max(rho_dict[key]) > ymax:
ymax = np.max(rho_dict[key])
ax.errorbar(X[key],
rho_dict[key],
yerr=Err[key],
label='%2.1f-%2.1f'%(m_range[key][0],m_range[key][1]),
fmt='-o', markersize=8,color=col,marker=mk,markerfacecolor=fl,markeredgewidth=0.7,
linewidth=.5,
barsabove=None,capsize=5,capthick=1,elinewidth=1
)
(ylo,yhi)=(10**np.floor(np.log10(ymin)),\
# 10**np.ceil(np.log10(ymax)))
ymax)
xc=(xmin*xmax)**.5
xlo = xc/(yhi/ylo)**.5
xhi = xc*(yhi/ylo)**.5
ax.axis([xlo,xhi,ylo,yhi])
#--- add major xticks
xmin=np.ceil(np.log10(ax.axis()[0]))
xmax=np.floor(np.log10(ax.axis()[1]))
nbin = xmax - xmin
ax.set_xticks(np.logspace(xmin,xmax,int(nbin)+1))
#--- add major yticks
ymin=np.ceil(np.log10(ax.axis()[2]))
ymax=np.floor(np.log10(ax.axis()[3]))
nbin = ymax - ymin
ax.set_yticks(np.logspace(ymin,ymax,int(nbin)+1))
#--- put minor bins
locmin = matplotlib.ticker.LogLocator(base=10.0,subs=(0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1),numticks=12)
ax.xaxis.set_minor_locator(locmin)
ax.xaxis.set_minor_formatter(matplotlib.ticker.NullFormatter())
ax.xaxis.set_major_formatter(MyLogFormatter()) #--- minus sign too long
#--- put minor bins y
locmin = matplotlib.ticker.LogLocator(base=10.0,subs=(0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1),numticks=12)
ax.yaxis.set_minor_locator(locmin)
ax.yaxis.set_minor_formatter(matplotlib.ticker.NullFormatter())
ax.yaxis.set_major_formatter(MyLogFormatter())
#fig.legend(title='m',prop=fontP,loc='lower left',frameon=False)#, bbox_to_anchor=(0.4, .6))
#ax.tick_params(axis='y',left=True, right=True,which='both')
#ax.tick_params(axis='x',bottom=True, top=True,which='both')
DrawFrame(ax, (0.22,0.06),(0.14,0.06),0.01,LOG_X=True,LOG_Y=True)
#plt.tight_layout()
#plt.savefig('%s/rho_t.png'%DIR_OUTPT_figs,dpi=300,bbox_inches='tight',transparent=True)
plt.show()
$\lambda(t)$ vs. $t$¶
In [90]:
#--- density plots: rho(r) (paper version 2nd)
def returnCMtoInch(x,y):
return (x/2.54,y/2.54)
fig, ax = plt.subplots(figsize=(4,4))
#---
ax.spines['right'].set_visible(False) #--- half open
ax.spines['top'].set_visible(False)
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
#---
ax.axis([10/(6e3/2e-3),10,2e-3,6e3])
ax.loglog()
#--- add major xticks
xmin=np.ceil(np.log10(ax.axis()[0]))
xmax=np.floor(np.log10(ax.axis()[1]))
nbin = xmax - xmin
ax.set_xticks(np.logspace(xmin,xmax,int(nbin)+1))
#--- add major yticks
ymin=np.ceil(np.log10(ax.axis()[2]))
ymax=np.floor(np.log10(ax.axis()[3]))
nbin = ymax - ymin
ax.set_yticks(np.logspace(ymin,ymax,int(nbin)+1))
#--- put minor bins
locmin = matplotlib.ticker.LogLocator(base=10.0,subs=(0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1),numticks=12)
ax.xaxis.set_minor_locator(locmin)
ax.xaxis.set_minor_formatter(matplotlib.ticker.NullFormatter())
#--- put minor bins y
locmin = matplotlib.ticker.LogLocator(base=10.0,subs=(0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1),numticks=12)
ax.yaxis.set_minor_locator(locmin)
ax.yaxis.set_minor_formatter(matplotlib.ticker.NullFormatter())
ax.set_xlabel(r'$t(day)$')
ax.set_ylabel(r'$\lambda(t)$')
#plt.xlim(1e-5,1e0)
#plt.ylim(1e-5,1e0)
#colors = ['black','red','green','blue','cyan']
#fillstyles=['white',None,'white',None,'white',None]
#markers=['o','s','D','^','<']
for key,col,mk,fl in zip(X,colors,markers,fillstyles):
xlabel = r'$%2.1f-%2.1f$'%(m_range[key][0],m_range[key][1])
if key == 5:
xlabel = r'$6.4$'
if key == 7:
xlabel = r'$7.1$'
ax.errorbar(X[key],
rho_dict[key],
yerr=Err[key],
label=xlabel,
fmt='-o', markersize=8,color=col,marker=mk,markerfacecolor=fl,markeredgewidth=0.7,
linewidth=.5,
barsabove=None,capsize=5,capthick=1,elinewidth=1
)
# ax.legend(title=r'$m$',prop=fontP,loc='lower left',frameon=False,
# bbox_to_anchor=(1, 0))
#ax.tick_params(axis='y',left=True, right=True,which='both')
#ax.tick_params(axis='x',bottom=True, top=True,which='both')
DrawFrame(ax, (0.22,0.06),(0.14,0.06),0.1,LOG_X=True,LOG_Y=True)
#plt.tight_layout()
#plt.savefig('%s/rho_t.png'%DIR_OUTPT_figs,dpi=75,bbox_inches='tight',transparent=True)
rescaled $\lambda(t)$ vs. $t$¶
In [91]:
#--- density plots: rho(r) (paper version 2nd)
def returnCMtoInch(x,y):
return (x/2.54,y/2.54)
fig, ax = plt.subplots(figsize=(4,4))
#---
ax.spines['right'].set_visible(False) #--- half open
ax.spines['top'].set_visible(False)
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
#---
ax.axis([10/(6e3/2e-3),10,2e-3,6e3])
ax.loglog()
#--- add major xticks
xmin=np.ceil(np.log10(ax.axis()[0]))
xmax=np.floor(np.log10(ax.axis()[1]))
nbin = xmax - xmin
ax.set_xticks(np.logspace(xmin,xmax,int(nbin)+1))
#--- add major yticks
ymin=np.ceil(np.log10(ax.axis()[2]))
ymax=np.floor(np.log10(ax.axis()[3]))
nbin = ymax - ymin
ax.set_yticks(np.logspace(ymin,ymax,int(nbin)+1))
#--- put minor bins
locmin = matplotlib.ticker.LogLocator(base=10.0,subs=(0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1),numticks=12)
ax.xaxis.set_minor_locator(locmin)
ax.xaxis.set_minor_formatter(matplotlib.ticker.NullFormatter())
#--- put minor bins y
locmin = matplotlib.ticker.LogLocator(base=10.0,subs=(0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1),numticks=12)
ax.yaxis.set_minor_locator(locmin)
ax.yaxis.set_minor_formatter(matplotlib.ticker.NullFormatter())
#--- rescaled
alpha_c = 0.0 #0.5
alpha_p = 0.6 #--- productivity
alpha_y = alpha_c - alpha_p
p = 1
plt.xlabel(r'$t(day)$')
plt.ylabel(r'$\lambda(t) \times t^{%s}$'%(p))
#plt.xlim(1e-5,1e0)
#plt.ylim(1e-5,1e0)
#colors = ['black','red','green','blue','cyan']
#fillstyles=['white',None,'white',None,'white',None]
#markers=['o','s','D','^','<']
for key,col,mk,fl in zip(X,colors,markers,fillstyles):
xlabel = r'$%2.1f-%2.1f$'%(m_range[key][0],m_range[key][1])
if key == 5:
xlabel = r'$6.4$'
if key == 7:
xlabel = r'$7.1$'
ax.errorbar(X[key],
rho_dict[key]*X[key]**p,
yerr=Err[key]*X[key]**p,
label=xlabel,
fmt='-o', markersize=8,color=col,marker=mk,markerfacecolor=fl,markeredgewidth=0.7,
linewidth=.5,
barsabove=None,capsize=5,capthick=1,elinewidth=1
)
ax.legend(title=r'$m$',prop=fontP,loc='lower left',frameon=False,
bbox_to_anchor=(1, 0))
#ax.tick_params(axis='y',left=True, right=True,which='both')
#ax.tick_params(axis='x',bottom=True, top=True,which='both')
DrawFrame(ax, (0.22,0.06),(0.14,0.06),0.1,LOG_X=True,LOG_Y=True)
#plt.tight_layout()
#plt.savefig('%s/rho_t_rescaled.png'%DIR_OUTPT_figs,dpi=300,bbox_inches='tight',transparent=True)
In [92]:
#--- construct trees
from math import *
class tree():
leafDepth = 0
n_leaves = 0
g_netx = None
leaf_generation = {} #--- key: leaf id; val: generation
nsize = 1 #--- cluster size
rtm_dic = {}
#---
def __init__( self, data, coord, coord_parent, n_generation ):
self.data = data #--- id
self.coord = coord
self.coord_parent = coord_parent
self.n_daughters = 0
self.daughter_obj = {}
self.n_generation = n_generation
#---
def insert( self, data, parent_id, coord, coord_parent, n_generation ):
if parent_id == self.data: #--- parent exists
self.daughter_obj[ self.n_daughters ] = tree( data, coord, coord_parent, n_generation )
self.n_daughters += 1
return
else:
for keys in self.daughter_obj:
self.daughter_obj[ keys ].insert( data, parent_id, coord, coord_parent, n_generation )
#---
def sprint( self, df ):
for keys in self.daughter_obj:
tree.g_netx.add_node(self.daughter_obj[ keys ].data)
tree.g_netx.add_edge( self.data, self.daughter_obj[ keys ].data)
self.daughter_obj[ keys ].sprint( df )
#---
def getLeaves( self ):
if len( self.daughter_obj ) == 0: #--- it's a leaf
tree.leaf_generation[ self.data ] = self.n_generation
else:
for keys in self.daughter_obj: #--- search in daughters
self.daughter_obj[ keys ].getLeaves()
#---
def getSize( self ):
for keys in self.daughter_obj: #--- search in daughters
tree.nsize += 1
self.daughter_obj[ keys ].getSize()
def get( self, title ):
pass
def get_coords( self ): #--- rtm_dic['node_id'] = [r,t,m]
for keys in self.daughter_obj:
child_object = self.daughter_obj[keys]
cords = child_object.coord
id_node = child_object.data
tree.rtm_dic[ id_node ] = cords
child_object.get_coords()
def plot(self,ax):
# print 'id=%s'%(self.data), 'generation=%s'%(self.n_generation)
for keys in self.daughter_obj:
child_object = self.daughter_obj[keys]
cords = child_object.coord
tree.pairs.append(child_object.data) #[self.coord, child_object.coord])
# ax.annotate("", tuple(cords[1][:2]), xytext=tuple(self.coord[1][:2]),
# textcoords='data', annotation_clip=False,
# arrowprops=dict(arrowstyle="-|>,head_width=.1,head_length=.4",color="b",linewidth="0.3"))
child_object.plot(ax)
def nodeExist(self, event_id):
if self.data == event_id:
# print 'yes'
return True
for keys in self.daughter_obj:
child_object = self.daughter_obj[keys]
if child_object.nodeExist( event_id ):
return True
return False
pref = 1.0 / (24.0*60*60)
#--------------------
#----- subset (the same as trig. analysis)
#--------------------
swarm_lohi = DataFrameSubSet( swarm, #--- complete catalog
'magnitude',
( mc, sys.maxint ) )
swarm_lohi = GetCartesian( swarm_lohi )
swarm_lohi.reset_index(inplace=True,drop=True)
NoTriggerList = set(nij_trig['Parent_id'])-set(nij_trig['Event_id']) #--- list of roots
#---
#--- include parent and entire generation
#---
CLUSTER={}
clusterID = 0
stree = {}
magScale = 1.0
for rootID in NoTriggerList: #--- roots: events with no parents
tree_level = 0
mainShockList = [ rootID ]
CLUSTER[clusterID]=[mainShockList[0]]
t_root = swarm_lohi.loc[ rootID ]['date']
r_root = swarm_lohi.loc[ rootID ][['x(km)','y(km)','z(km)']].tolist()
m_root = swarm_lohi.loc[ rootID ]['magnitude']
stree[ clusterID ] = tree( rootID, [ t_root, r_root, m_root ],
[ t_root, r_root, m_root ],
tree_level )
while len(mainShockList): #--- from root down to leaves
newMainShockList = []
for mainShockID, counter in zip( mainShockList, xrange( sys.maxint ) ):
try:
newMainShockList += d_trig[ mainShockID ] #--- aftershocks become new
except:
# traceback.print_exc()
continue
for aftershockID in d_trig[ mainShockID ]:
CLUSTER[ clusterID ].append(aftershockID)
# dt = (swarm_lohi.loc[ aftershockID ]['date']-swarm_lohi.loc[ rootID ]['date']).total_seconds() * pref
t_afs = swarm_lohi.loc[ aftershockID ]['date']
# -swarm_lohi.loc[ rootID ]['date']).total_seconds() * pref
r_afs = swarm_lohi.loc[aftershockID][['x(km)','y(km)','z(km)']].tolist()
m_afs = swarm_lohi.loc[aftershockID]['magnitude']
t_parent = swarm_lohi.loc[ mainShockID ]['date']
r_parent = swarm_lohi.loc[mainShockID][['x(km)','y(km)','z(km)']].tolist()
m_parent = swarm_lohi.loc[mainShockID]['magnitude']
stree[ clusterID ].insert( aftershockID, mainShockID,
[t_afs, r_afs, m_afs],
[t_parent, r_parent, m_parent],
tree_level + 1 )
mainShockList = [ i for i in newMainShockList ]
tree_level += 1
assert len(mainShockList) == 0 #--- leaf
clusterID+=1
sl=[]
for keys in stree:
sl.append([stree[keys].n_daughters,stree[keys].data,keys])
sl.sort(reverse=True)
sl[:3]
Out[92]:
In [93]:
x=(-97,-96.5)
y=(35.8,36)
swarm_lohi.sort_values(by='magnitude',ascending=False).head() #[(swarm_lohi['longitude']>x[0]) & (swarm_lohi['longitude']<x[1]) & (swarm_lohi['latitude']>y[0]) & (swarm_lohi['latitude']<y[1])].head(n=10)
Out[93]:
In [94]:
#--- a large event belongs to what cluster
event_id = 5 #1509
FOUND = False
for item in sl:
cls_id = item[2]
root_id = item[1]
if stree[cls_id].nodeExist(event_id):
FOUND = True
break
if FOUND:
print 'root_id=%s'%root_id
else:
print 'it is a background event'
In [95]:
#--- leaf vs. depth
import networkx as nx
#import treeDataStruct as tds
from itertools import count
import random as rnd
exp = 4
for item, index in zip(sl[:6],xrange(sys.maxint)):
sid = item[2]
root_id = item[1]
# print 'root_id=',root_id
tree.g_netx = None
tree.g_netx = nx.DiGraph(directed=True)
tree.g_netx.add_node(stree[ sid ].data,color='b')
stree[ sid ].sprint(swarm_lohi )
# read edgelist from grid.edgelist
nx.write_edgelist(tree.g_netx, path="grid.edgelist", delimiter=":")
H = nx.read_edgelist(path="grid.edgelist", delimiter=":") #,create_using=nx.DiGraph())
# nx.draw(H,with_labels=True,arrows = True)#pos=nx.spring_layout(H))
# nx.draw_networkx(tree.g_netx, arrows=True, with_labels=True,node_color='b') #, **kwds)
pos = nx.spring_layout(H)
nodes=H.nodes
colors = ['red' for n in nodes]
sizes=[exp**swarm_lohi.loc[ int(n) ]['magnitude'] for n in nodes]
for n,indx in zip(nodes,xrange(sys.maxint)):
if int(n) == root_id:
colors[indx] = 'gray'
ec = nx.draw_networkx_edges(H, pos, alpha=0.2,arrows = True)
nc = nx.draw_networkx_nodes(H, pos,node_size=sizes, node_color=colors,cmap=plt.cm.seismic) #, nodelist=nodes, ,
# with_labels=False, node_size=100, cmap=plt.cm.jet)
plt.axis('off')
# plt.savefig('%s/topology.%s.png'%(DIR_OUTPT_figs,index),dpi=75)#,bbox_inches='tight')
plt.show()
size vs. depth¶
In [96]:
mpl.rcParams.update(mpl.rcParamsDefault)
warnings.filterwarnings('ignore') #--- get rid of warnings
rc('text', usetex=True)
font = {'size' : 26}
matplotlib.rc('font', **font)
fig = plt.figure(figsize=(4,4))
ax = fig.add_subplot(111)
ax.set_xscale('linear')
ax.set_yscale('log')
#ax.set_xlabel('mean depth')
#ax.set_ylabel('size')
ax.axis([0,7.0,1,1e2])
ax.set_yscale('log')
#--- add major xticks
xmin=np.ceil(ax.axis()[0])
xmax=np.floor(ax.axis()[1])
nbin = xmax - xmin
ax.set_xticks(np.linspace(ax.axis()[0],ax.axis()[1],int(nbin)+1))
#--- add major yticks
ymin=np.ceil(np.log10(ax.axis()[2]))
ymax=np.floor(np.log10(ax.axis()[3]))
nbin = ymax - ymin
ax.set_yticks(np.logspace(ymin,ymax,int(nbin)+1))
MD=[]
S=[]
M=[]
root=[]
for item in sl:
sid = item[2]
root_id = item[1]
root.append(root_id)
tree.leaf_generation={} #--- initialize
# stree[ sid ].initialize()
stree[ sid ].getLeaves() #--- call function
d = stree[ sid ].leaf_generation
# print 'd[%s]=%s'%(sid,d)
mean_depth = np.mean( d.values() ) #np.mean( d.values() ) #1.0 * tds.tree.leafDepth / tds.tree.n_leaves
#--- size
tree.nsize = 1 #--- initialize
stree[ sid ].getSize() #--- call function
MD.append(mean_depth)
S.append(stree[ sid ].nsize)
M.append(swarm_lohi.loc[stree[ sid ].data]['magnitude'])
exp = 5*.7
S=np.array(S)
MD = np.array(MD)
M=np.array(M)
root=np.array(root)
scatter=ax.scatter(MD, S,
marker='o',color='gray',edgecolors='none',alpha=0.5,
s=exp**np.array(M))
#--- color specific clusters
cond = np.all([S>=5,MD>0.0],axis=0)
scatter=ax.scatter(MD[cond], S[cond],
marker='o',color='red',edgecolors='none',#alpha=0.5,
s=exp**np.array(M[cond]))
#print root[10<=S], S[10<=S]
print 'roots=',root[cond]
print 'size',S[cond]
print 'depth',MD[cond]
# #--- legend
# M=np.array(M)
# m_min=M.min()
# m_max=M.max()
# m_mean=(m_min+m_max)/2 #M.mean()
# l1 = plt.scatter([-2],[-2], s=exp**m_min, c='gray',edgecolors='none')
# l2 = plt.scatter([-3],[-3], s=exp**m_mean,c='gray', edgecolors='none')
# l3 = plt.scatter([-4],[-4], s=exp**m_max,c='gray', edgecolors='none')
# labels = ["%2.1f"%m_min, "%2.1f"%m_mean, "%2.1f"%m_max]
# leg = plt.legend([l1, l2, l3], labels, ncol=3,fontsize=16, frameon=False,
# handlelength=0, borderpad = 0, labelspacing=0,columnspacing=2,prop=None,
# handletextpad=1, scatterpoints = 1,loc='upper right', bbox_to_anchor=(.92, 0.95))
#--- frame
DrawFrame(ax, (0.24,0.08),(0.14,0.06),0.1,LOG_Y=True)
#--- save
#plt.savefig('%s/topology.png'%DIR_OUTPT_figs,dpi=300,bbox_inches='tight')
mpl.rcParams.update(mpl.rcParamsDefault)
warnings.filterwarnings('ignore') #--- get rid of warnings
rc('text', usetex=True)
font = {'size' : 26}
matplotlib.rc('font', **font)
trig. cascades¶
In [97]:
#--- leaf vs. depth
import networkx as nx
#import treeDataStruct as tds
from itertools import count
import random as rnd
#dd={'ROOT':407,
# 'exponent':4.0*2.7}
#dd={'ROOT':325,
# 'exponent':4.0*2.7}
dd={'ROOT':1,#1505,
'exponent':4.0*.8}
#for ii in xrange(1):
ROOT = dd['ROOT']
exponent=dd['exponent']
for item in sl:
cls_id = item[2]
root_id = item[1]
if root_id != ROOT:
continue
tree.pairs = []
stree[cls_id].plot(ax)
tree.pairs = [root_id]+tree.pairs
for item in sl:
sid = item[2]
root_id = item[1]
if root_id != ROOT:
continue
print 'root_id=',root_id, 'n=%s'%(item[0])
tree.g_netx = None
tree.g_netx = nx.DiGraph(directed=True)
tree.g_netx.add_node(stree[ sid ].data,color='b')
stree[ sid ].sprint(swarm_lohi )
# read edgelist from grid.edgelist
nx.write_edgelist(tree.g_netx, path="grid.edgelist", delimiter=":")
H = nx.read_edgelist(path="grid.edgelist", delimiter=":") #,create_using=nx.DiGraph())
# nx.draw(H,with_labels=True,arrows = True)#pos=nx.spring_layout(H))
# nx.draw_networkx(tree.g_netx, arrows=True, with_labels=True,node_color='b') #, **kwds)
pos = nx.spring_layout(H)
nodes=H.nodes
colors = ['red' for n in nodes]
sizes=[exponent**swarm_lohi.loc[ int(n) ]['magnitude'] for n in nodes]
node_shape = ['o' for n in nodes]
for n,indx in zip(nodes,xrange(sys.maxint)):
if int(n) == root_id:
colors[indx] = 'yellow'
# node_shape[indx]='*'
fig=plt.figure(figsize=(8,8))
ax=fig.add_subplot(111)
ec = nx.draw_networkx_edges(H, pos, alpha=0.2,arrows = True, ax= ax,edge_color='b',width=3)
nc = nx.draw_networkx_nodes(H, pos,node_size=sizes, node_color=colors,cmap=plt.cm.seismic, ax=ax,
edgecolors='black',node_shape='o') #, nodelist=nodes, ,
# with_labels=False, node_size=100, cmap=plt.cm.jet)
plt.axis('on')
ax.tick_params(labelbottom=False,labelleft=False,length=0.0)
fig.show()
# DrawFrame(ax, (0.0,0.0),(0.0,0.0),.1)
# DrawFrame(ax, (0.16,0.16),(0.07,0.03),0.1)
DrawFrame(ax, (0.16,0.1),(0.09,0.03),0.1)
#plt.tight_layout()
# fig.savefig('%s/tree.png'%DIR_OUTPT_figs,dpi=300,bbox_inches='tight',transparent=True)
timeseries associated with the trig. cascade¶
In [98]:
#--- plot clusters
def Inside(t,(tmin,tmax)):
if tmin<= t<tmax:
return True
return False
def GetTrigList( nij_trig ):
d_trig = {}
for items in nij_trig.itertuples():
triggerID = items.Parent_id
d_trig.setdefault( triggerID, [] ).append( items.Event_id )
return d_trig
def PlotArrowsTime(df_complete,d_trig, (tmin,tmax), (xmin,xmax), (ymin,ymax) ):
tlist=[]
mlist=[]
xm = []
ym = []
for triggerID in d_trig: #--- mother events
t0 = df_complete['date'].iloc[ triggerID ] #--- time of mother event
m0 = df_complete['magnitude'].iloc[triggerID] #--- magnitude
if not ( Inside(t0,(tmin,tmax) ) and #--- within the given interval
Inside(swarm_lohi['x(km)'].iloc[triggerID],(xmin,xmax)) and
Inside(swarm_lohi['y(km)'].iloc[triggerID],(ymin,ymax)) ):
continue
# x0 = md.date2num( t0 ) #--- convert to time object
# y0 = m0 #--- magnitude
# tlist.append( t0 )
# mlist.append( m0 )
for daughter_id in d_trig[triggerID]: #--- children
t1 = df_complete['date'].iloc[ daughter_id ] #--- time
m1 = df_complete['magnitude'].iloc[ daughter_id ] #--- magnitude
if not ( Inside(t1,(tmin,tmax) ) and #--- within the given interval
Inside(swarm_lohi['x(km)'].iloc[daughter_id],(xmin,xmax)) and
Inside(swarm_lohi['y(km)'].iloc[daughter_id],(ymin,ymax)) ):
continue
# x1 = md.date2num( t1 ) #--- convert to time object
# y1 = m1 #--- magnitude
# xw = x1 - x0 #--- t_child-t_parent
# yw = y1 - y0 #--- m_child - m_parent
if daughter_id in tree.pairs:
tlist.append( t1 )
mlist.append( m1 )
ax.annotate("", (t1,m1), xytext=(t0, m0), zorder=1,
textcoords='data',clip_on=True,
arrowprops=dict(arrowstyle="-|>,head_width=%s,head_length=%s"%(head_width,head_length),
shrinkA=shrinkA,
color="b",linewidth="0.3"))
#--- plot mother
if triggerID == tree.pairs[0]: #in roott:
xm.append(t0)
ym.append(m0)
#--- plot circles
df=pd.DataFrame({'date':tlist,'mag':mlist})
ax.scatter(df['date'], df['mag'],
s=exponent**(df['mag']),
alpha=1,zorder=2,
facecolors='red',color='black')
#plt.savefig('timeSeries.png')
for x0,y0 in zip(xm,ym):
# print x0,y0
ax.scatter(x0,y0,
s=exponent**y0,
marker='*', zorder=3,
facecolors='yellow',color='black',
alpha=1.0)
#--------------------------------------
#----- key: event value: aftershock id
#--------------------------------------
d_trig = GetTrigList( nij_trig )
# #--------------------
# #----- subset (the same as trig. analysis)
# #--------------------
# swarm_lohi = DataFrameSubSet( swarm, #--- complete catalog
# 'magnitude',
# ( mc, sys.maxint ) )
# swarm_lohi.reset_index(inplace=True,drop=True)
# #--------------------
# #--- cartesian coords
# #--------------------
# swarm_lohi = GetCartesian( swarm_lohi )
# dd={'ROOT':407,
# 'exponent':4.5*3.2,
# 'dt_before':0.005,'dt_after':.1,
# 'head_width':.2,'head_length':.4,
# 'shrinkA':0}
# dd={'ROOT':325,
# 'exponent':4.5*3.2,
# 'dt_before':0.005,'dt_after':.1,
# 'head_width':.2,'head_length':.4,
# 'shrinkA':0}
dd={'ROOT':1,#1505,
'exponent':4.5*.8,
'dt_before':0.01,'dt_after':0.25*12,
'head_width':.2,'head_length':.4,
'shrinkA':0}
#for ii in xrange(1):
ROOT = dd['ROOT']
exponent=dd['exponent']
dt_before = dd['dt_before']
dt_after=dd['dt_after']
head_width = dd['head_width']
head_length=dd['head_length']
shrinkA=dd['shrinkA']
swarm_lohi = GetCartesian( swarm_lohi )
dff = swarm_lohi.sort_values('magnitude',ascending=False)
roott = [i[1] for i in sl]
#for item in dff.iloc[:30].itertuples(): #--- plot clusters associated with large events
for item in dff.itertuples(): #--- plot clusters associated with large events
if item.Index != ROOT:
continue
(xc,yc)=(item.longitude,item.latitude) #(-96.807159,35.985256) #(-98.739380,36.467762) #(-99.0,36.5)
tc = item.date #pd.to_datetime("2016-09-03 12:02:44.520")
dx = 1000
fig = plt.figure(figsize=(24,8),frameon=False) #, dpi=150)
ax = fig.add_subplot(111)
#--- plot all events
plt.ylim(mc,swarm_lohi['magnitude'].max())
plt.scatter(swarm_lohi['date'],swarm_lohi['magnitude'],
s=exponent**swarm_lohi['magnitude'],
alpha=0.1)
tt = tc #swarm_lohi['date'].loc[key_max]
xx={0:xc,1:yc}
PlotArrowsTime( swarm_lohi, d_trig,
( tt+datetime.timedelta(days=-dt_before),tt+datetime.timedelta(days=+dt_after)),
(xx[0]-dx,xx[0]+dx),
(xx[1]-dx,xx[1]+dx) )
# ax.set_xlim(tt+datetime.timedelta(days=-dt_before),swarm_lohi.iloc[tree.pairs]['date'].max())
ax.set_xlim(tt+datetime.timedelta(days=-dt_before),tt+datetime.timedelta(days=+dt_after))
ax.set_ylim(mc-0.1,7.5)
ax.tick_params(axis='y',labelsize=32,right=True)
ax.tick_params(axis='x',rotation=20,labelsize=28,top=True)
ax.xaxis.set_major_formatter(dates.DateFormatter('%d %b %Y \n %H:%M'))
#--- frame
DrawFrame(ax, (0.04,0.04),(0.22,0.04),0.1)
# fig.savefig('%s/timeSeries.png'%DIR_OUTPT_figs,bbox_inches='tight',dpi=150)
spatial map associated with the trig. cascade¶
In [99]:
#--- plot clusters
def Inside(t,(tmin,tmax)):
if tmin<= t<tmax:
return True
return False
def GetTrigList( nij_trig ):
d_trig = {}
for items in nij_trig.itertuples():
triggerID = items.Parent_id
d_trig.setdefault( triggerID, [] ).append( items.Event_id )
return d_trig
def PlotArrowsSpace(df_complete,d_trig, (tmin,tmax), (xmin,xmax), (ymin,ymax) ):
xlist=[]
ylist=[]
mlist=[]
xm=[]
ym=[]
m_mother=[]
for triggerID in d_trig: #--- mother events
t0 = df_complete['date'].iloc[ triggerID ] #--- time of mother event
( x0, y0 ) = ( swarm_lohi['longitude'].iloc[triggerID],
swarm_lohi['latitude'].iloc[triggerID] )
m0 = df_complete['magnitude'].iloc[triggerID] #--- magnitude
if not ( #Inside(t0,(tmin,tmax) ) and #--- within the given interval
Inside(x0,(xmin,xmax)) and
Inside(y0,(ymin,ymax)) ):
continue
for daughter_id in d_trig[triggerID]: #--- children
t1 = df_complete['date'].iloc[ daughter_id ] #--- time
( x1, y1 ) = ( swarm_lohi['longitude'].iloc[ daughter_id ],
swarm_lohi['latitude'].iloc[ daughter_id ] )
m1 = df_complete['magnitude'].iloc[ daughter_id ] #--- magnitude
if not ( #Inside(t1,(tmin,tmax) ) and #--- within the given interval
Inside(x1,(xmin,xmax)) and
Inside(y1,(ymin,ymax)) ):
continue
if daughter_id in tree.pairs:
xlist.append( x1 )
ylist.append( y1 )
mlist.append( m1 )
ax.annotate("", (x1,y1), xytext=(x0, y0), zorder=1,
textcoords='data', annotation_clip=False,
# arrowprops=dict(width=.2,headlength=.4,shrink=0.5,color='b'))
# backgroundcolor="w",
arrowprops=dict(arrowstyle="-|>,head_width=%s,head_length=%s"%(head_width,head_length),
shrinkA=shrinkA,
color="b",linewidth="0.3"))
#--- plot mother
if triggerID == tree.pairs[0]: # in roott:
xm.append(x0)
ym.append(y0)
m_mother.append(m0)
#--- plot circles
df=pd.DataFrame({'x(km)':xlist,'y(km)':ylist,'m':mlist})
ax.scatter(df['x(km)'], df['y(km)'],
s=exponent**(df['m']),
alpha=1, zorder=2,
facecolors='red',color='black')
for x0,y0,m0 in zip(xm,ym,m_mother):
plt.scatter(x0,y0,
s=exponent**m0,
marker='*',zorder=3,
facecolors='yellow',color='black',
alpha=1.0)
# #--------------------------------------
# #----- key: event value: aftershock id
# #--------------------------------------
# d_trig = GetTrigList( nij_trig )
# #--------------------
# #----- subset (the same as trig. analysis)
# #--------------------
# swarm_lohi = DataFrameSubSet( swarm, #--- complete catalog
# 'magnitude',
# ( mc, sys.maxint ) )
# swarm_lohi.reset_index(inplace=True,drop=True)
# #--------------------
# #--- cartesian coords
# #--------------------
# swarm_lohi = GetCartesian( swarm_lohi )
# dd={'ROOT':407,
# 'exponent':4.0*2.7,
# 'dx':max(swarm_lohi.iloc[tree.pairs]['longitude'].max()-swarm_lohi.iloc[tree.pairs[0]]['longitude'],
# swarm_lohi.iloc[tree.pairs]['latitude'].max()-swarm_lohi.iloc[tree.pairs[0]]['latitude']),
# 'head_width':.15,'head_length':.3,
# 'shrinkA':0}
# dd={'ROOT':325,
# 'exponent':4.0*2.7,
# 'dx':max(swarm_lohi.iloc[tree.pairs]['longitude'].max()-swarm_lohi.iloc[tree.pairs[0]]['longitude'],
# swarm_lohi.iloc[tree.pairs]['latitude'].max()-swarm_lohi.iloc[tree.pairs[0]]['latitude']),
# 'head_width':.15,'head_length':.3,
# 'shrinkA':0}
dd={'ROOT':1505,
'exponent':4.0*0.8,
'dx':max(swarm_lohi.iloc[tree.pairs]['longitude'].max()-swarm_lohi.iloc[tree.pairs[0]]['longitude'],
swarm_lohi.iloc[tree.pairs]['latitude'].max()-swarm_lohi.iloc[tree.pairs[0]]['latitude']),
'head_width':.15,'head_length':.3,
'shrinkA':0}
#for ii in xrange(1):
ROOT = dd['ROOT']
exponent=dd['exponent']
dx = dd['dx']
head_width = dd['head_width']
head_length=dd['head_length']
shrinkA=dd['shrinkA']
#--- plot arrows
#for ii in xrange(1):
swarm_lohi = GetCartesian( swarm_lohi )
dff = swarm_lohi.sort_values('magnitude',ascending=False)
roott = [i[1] for i in sl]
#for item in dff.iloc[:30].itertuples(): #--- plot clusters associated with large events
for item in dff.itertuples(): #--- plot clusters associated with large events
if item.Index != ROOT:
continue
(xc,yc)=(item.longitude,item.latitude) #(-96.807159,35.985256) #(-98.739380,36.467762) #(-99.0,36.5)
tc = item.date #pd.to_datetime("2016-09-03 12:02:44.520")
dt = 1000 #--- setup
fig = plt.figure(figsize=(8,8)) #,frameon=False) #, dpi=300)
ax = fig.add_subplot(111)
#--- plot all events
ax.scatter(swarm_lohi['longitude'], swarm_lohi['latitude'], # 'x(km)'],swarm_lohi['y(km)'],
s=exponent**swarm_lohi['magnitude'],
alpha=0.1)
tt = tc #swarm_lohi['date'].loc[key_max]
xx={0:xc,1:yc}
PlotArrowsSpace( swarm_lohi, d_trig,
( tt+datetime.timedelta(days=-dt),tt+datetime.timedelta(days=+dt)),
(xx[0]-dx,xx[0]+dx),
(xx[1]-dx,xx[1]+dx) )
ax.set_xlim(xx[0]-dx,xx[0]+dx)
ax.set_ylim(xx[1]-dx,xx[1]+dx)
#--- set tick labels
xlist=np.linspace(xx[0]-dx,xx[0]+dx,4,endpoint=True)
ax.set_xticks(xlist)
xlist=[r'$%5.3f^{\circ}$'%i for i in xlist]
#
ylist=np.linspace(xx[1]-dx,xx[1]+dx,4,endpoint=True)
ax.set_yticks(ylist)
ylist=[r'$%5.3f^{\circ}$'%i for i in ylist]
# ax.set_yticklabels(ylist)
ax.tick_params(labelsize=24)
ax.tick_params(axis='y',labelright=True,labelleft=False,right=True,left=True)
ax.tick_params(axis='x',top=True)#,left=True)
ax.set_xticklabels(xlist,{'fontsize':20})
ax.set_yticklabels(ylist,{'fontsize':20})
#--- frame
# DrawFrame(ax, (0.16,0.16),(0.07,0.03),0.1)
DrawFrame(ax, (0.1,0.16),(0.09,0.03),0.1)
#fig.savefig('%s/spatialMap.png'%DIR_OUTPT_figs,bbox_inches='tight',dpi=150)
spatial map associated with the trig. cascade¶
In [100]:
#--- plot clusters
def Inside(t,(tmin,tmax)):
if tmin<= t<tmax:
return True
return False
def GetTrigList( nij_trig ):
d_trig = {}
for items in nij_trig.itertuples():
triggerID = items.Parent_id
d_trig.setdefault( triggerID, [] ).append( items.Event_id )
return d_trig
def PlotArrowsSpace(df_complete,d_trig, (tmin,tmax), (xmin,xmax), (ymin,ymax) ):
xlist=[]
ylist=[]
mlist=[]
tlist=[]
xm=[]
ym=[]
m_mother=[]
tm=[]
for triggerID in d_trig: #--- mother events
t0 = df_complete['date'].iloc[ triggerID ] #--- time of mother event
( x0, y0 ) = ( swarm_lohi['longitude'].iloc[triggerID],
swarm_lohi['latitude'].iloc[triggerID] )
m0 = df_complete['magnitude'].iloc[triggerID] #--- magnitude
if not ( #Inside(t0,(tmin,tmax) ) and #--- within the given interval
Inside(x0,(xmin,xmax)) and
Inside(y0,(ymin,ymax)) ):
continue
for daughter_id in d_trig[triggerID]: #--- children
t1 = df_complete['date'].iloc[ daughter_id ] #--- time
( x1, y1 ) = ( swarm_lohi['longitude'].iloc[ daughter_id ],
swarm_lohi['latitude'].iloc[ daughter_id ] )
m1 = df_complete['magnitude'].iloc[ daughter_id ] #--- magnitude
if not ( #Inside(t1,(tmin,tmax) ) and #--- within the given interval
Inside(x1,(xmin,xmax)) and
Inside(y1,(ymin,ymax)) ):
continue
if daughter_id in tree.pairs:
xlist.append( x1 )
ylist.append( y1 )
mlist.append( m1 )
tlist.append( t1 )
ax.annotate("", (x1,y1), xytext=(x0, y0), zorder=1,
textcoords='data', annotation_clip=False,
# arrowprops=dict(width=.2,headlength=.4,shrink=0.5,color='b'))
# backgroundcolor="w",
arrowprops=dict(arrowstyle="-|>,head_width=%s,head_length=%s"%(head_width,head_length),
shrinkA=shrinkA,
color="b",linewidth="0.3"))
#--- plot mother
if triggerID == tree.pairs[0]: # in roott:
xm.append(x0)
ym.append(y0)
m_mother.append(m0)
tm.append(t0)
#--- plot circles
df=pd.DataFrame({'x(km)':xlist,'y(km)':ylist,'m':mlist,'t':tlist})
ax.scatter(df['x(km)'], df['y(km)'],
s=exponent**(df['m']),
alpha=.5, zorder=2,# c = df['t']-tm[0],cmap='jet')#,
facecolors='red',color='black')
for x0,y0,m0 in zip(xm,ym,m_mother):
plt.scatter(x0,y0,
s=exponent**m0,
marker='*',zorder=3,
facecolors='yellow',color='black',
alpha=1.0)
# #--------------------------------------
# #----- key: event value: aftershock id
# #--------------------------------------
# d_trig = GetTrigList( nij_trig )
# #--------------------
# #----- subset (the same as trig. analysis)
# #--------------------
# swarm_lohi = DataFrameSubSet( swarm, #--- complete catalog
# 'magnitude',
# ( mc, sys.maxint ) )
# swarm_lohi.reset_index(inplace=True,drop=True)
# #--------------------
# #--- cartesian coords
# #--------------------
# swarm_lohi = GetCartesian( swarm_lohi )
# dd={'ROOT':407,
# 'exponent':4.0*2.7,
# 'dx':max(swarm_lohi.iloc[tree.pairs]['longitude'].max()-swarm_lohi.iloc[tree.pairs[0]]['longitude'],
# swarm_lohi.iloc[tree.pairs]['latitude'].max()-swarm_lohi.iloc[tree.pairs[0]]['latitude']),
# 'head_width':.15,'head_length':.3,
# 'shrinkA':0}
# dd={'ROOT':325,
# 'exponent':4.0*2.7,
# 'dx':max(swarm_lohi.iloc[tree.pairs]['longitude'].max()-swarm_lohi.iloc[tree.pairs[0]]['longitude'],
# swarm_lohi.iloc[tree.pairs]['latitude'].max()-swarm_lohi.iloc[tree.pairs[0]]['latitude']),
# 'head_width':.15,'head_length':.3,
# 'shrinkA':0}
#--- plot arrows
#for ii in xrange(1):
swarm_lohi = GetCartesian( swarm_lohi )
dff = swarm_lohi.sort_values('magnitude',ascending=False)
roott = [i[1] for i in sl]
xxx=np.array(sl)
sr=[[j,i] for i,j in zip(root,S)]
sr.sort(reverse=True)
#sr[:10]
#for ROOT in root[cond]:
for ii in sr[:5]:
ROOT = ii[1]
# if not ROOT == 1:
# continue
cls_id = xxx[xxx[:,1]==ROOT][0][2]
tree.pairs = []
stree[cls_id].plot(ax)
tree.pairs = [ROOT]+tree.pairs
dd={'ROOT':ROOT,
'exponent':4.0*0.8,
# 'dx':max(swarm_lohi.iloc[tree.pairs]['longitude'].max()-swarm_lohi.iloc[tree.pairs[0]]['longitude'],
# swarm_lohi.iloc[tree.pairs]['latitude'].max()-swarm_lohi.iloc[tree.pairs[0]]['latitude']),
'dx':0.3*max(swarm_lohi['longitude'].max()-swarm_lohi['longitude'].min(),
swarm_lohi['latitude'].max()-swarm_lohi['latitude'].min()),
'head_width':.15,'head_length':.3,
'shrinkA':0}
exponent=dd['exponent']
dx = dd['dx']
head_width = dd['head_width']
head_length=dd['head_length']
shrinkA=dd['shrinkA']
#for ii in xrange(1):
#ROOT = dd['ROOT']
#for item in dff.iloc[:30].itertuples(): #--- plot clusters associated with large events
item = dff.loc[ROOT]
if 1:
# for item in dff.itertuples(): #--- plot clusters associated with large events
# if item.Index != ROOT:
# continue
(xc,yc)=(item['longitude'],item['latitude'])
# (xc,yc)=(swarm_lohi['longitude'].mean(),swarm_lohi['latitude'].mean())
tc = item['date'] #pd.to_datetime("2016-09-03 12:02:44.520")
dt = 1000 #--- setup
fig = plt.figure(figsize=(8,8)) #,frameon=False) #, dpi=300)
ax = fig.add_subplot(111)
#--- plot all events
ax.scatter(swarm_lohi['longitude'], swarm_lohi['latitude'], # 'x(km)'],swarm_lohi['y(km)'],
s=exponent**swarm_lohi['magnitude'],
alpha=0.1)
tt = tc #swarm_lohi['date'].loc[key_max]
xx={0:xc,1:yc}
PlotArrowsSpace( swarm_lohi, d_trig,
( tt+datetime.timedelta(days=-dt),tt+datetime.timedelta(days=+dt)),
(xx[0]-dx,xx[0]+dx),
(xx[1]-dx,xx[1]+dx) )
ax.set_xlim(xx[0]-dx,xx[0]+dx)
ax.set_ylim(xx[1]-dx,xx[1]+dx)
#--- set tick labels
xlist=np.linspace(xx[0]-dx,xx[0]+dx,4,endpoint=True)
ax.set_xticks(xlist)
xlist=[r'$%5.3f^{\circ}$'%i for i in xlist]
#
ylist=np.linspace(xx[1]-dx,xx[1]+dx,4,endpoint=True)
ax.set_yticks(ylist)
ylist=[r'$%5.3f^{\circ}$'%i for i in ylist]
# ax.set_yticklabels(ylist)
ax.tick_params(labelsize=24)
ax.tick_params(axis='y',labelright=True,labelleft=False,right=True,left=True)
ax.tick_params(axis='x',top=True)#,left=True)
ax.set_xticklabels(xlist,{'fontsize':20})
ax.set_yticklabels(ylist,{'fontsize':20})
#--- frame
# DrawFrame(ax, (0.16,0.16),(0.07,0.03),0.1)
DrawFrame(ax, (0.1,0.16),(0.09,0.03),0.1)
# fig.savefig('%s/spatialMap.%s.png'%(DIR_OUTPT_figs,ROOT),bbox_inches='tight',dpi=150)
plot separate clusters¶
In [101]:
#--- plot clusters
def Inside(t,(tmin,tmax)):
if tmin<= t<tmax:
return True
return False
def GetTrigList( nij_trig ):
d_trig = {}
for items in nij_trig.itertuples():
triggerID = items.Parent_id
d_trig.setdefault( triggerID, [] ).append( items.Event_id )
return d_trig
def PlotArrowsSpace(df_complete,d_trig, (tmin,tmax), (xmin,xmax), (ymin,ymax) ):
xlist=[]
ylist=[]
mlist=[]
tlist=[]
xm=[]
ym=[]
m_mother=[]
tm=[]
for triggerID in d_trig: #--- mother events
t0 = df_complete['date'].iloc[ triggerID ] #--- time of mother event
# ( x0, y0 ) = ( swarm_lohi['longitude'].iloc[triggerID],
# swarm_lohi['latitude'].iloc[triggerID] )
( X0, Y0 ) = ( swarm_lohi['x(km)'].iloc[triggerID],
swarm_lohi['y(km)'].iloc[triggerID] )
m0 = df_complete['magnitude'].iloc[triggerID] #--- magnitude
# if not ( #Inside(t0,(tmin,tmax) ) and #--- within the given interval
# Inside(X0,(xmin,xmax)) and
# Inside(Y0,(ymin,ymax)) ):
# continue
for daughter_id in d_trig[triggerID]: #--- children
t1 = df_complete['date'].iloc[ daughter_id ] #--- time
# ( x1, y1 ) = ( swarm_lohi['longitude'].iloc[ daughter_id ],
# swarm_lohi['latitude'].iloc[ daughter_id ] )
( X1, Y1 ) = ( swarm_lohi['x(km)'].iloc[ daughter_id ],
swarm_lohi['y(km)'].iloc[ daughter_id ] )
m1 = df_complete['magnitude'].iloc[ daughter_id ] #--- magnitude
# if not ( #Inside(t1,(tmin,tmax) ) and #--- within the given interval
# Inside(X1,(xmin,xmax)) and
# Inside(Y1,(ymin,ymax)) ):
# continue
if daughter_id in d_trig[ROOT]:
xlist.append( X1 )
ylist.append( Y1 )
mlist.append( m1 )
tlist.append( t1 )
ax.annotate("", (X1,Y1), xytext=(X0, Y0), zorder=1,
textcoords='data', annotation_clip=False,
# arrowprops=dict(width=.2,headlength=.4,shrink=0.5,color='b'))
# backgroundcolor="w",
arrowprops=dict(arrowstyle="-|>,head_width=%s,head_length=%s"%(head_width,head_length),
shrinkA=shrinkA,
color="b",linewidth="0.3"))
#--- plot mother
if triggerID == ROOT: #tree.pairs[0]: # in roott:
xm.append(X0)
ym.append(Y0)
m_mother.append(m0)
tm.append(t0)
#--- plot circles
df=pd.DataFrame({'x(km)':xlist,'y(km)':ylist,'m':mlist,'t':tlist})
ax.scatter(df['x(km)'], df['y(km)'],
s=exponent**(df['m']),
alpha=.5, zorder=2,# c = df['t']-tm[0],cmap='jet')#,
facecolors='red',color='black')
for x0,y0,m0 in zip(xm,ym,m_mother):
plt.scatter(x0,y0,
s=exponent**m0,
marker='*',zorder=3,
facecolors='yellow',color='black',
alpha=1.0)
print m_mother[0]
return (df['x(km)']-xm[0] + 1j*(df['y(km)']-ym[0])).abs(),df['t']-tm[0]
# #--------------------------------------
# #----- key: event value: aftershock id
# #--------------------------------------
d_trig = GetTrigList( nij_trig )
# #--------------------
# #----- subset (the same as trig. analysis)
# #--------------------
# swarm_lohi = DataFrameSubSet( swarm, #--- complete catalog
# 'magnitude',
# ( mc, sys.maxint ) )
# swarm_lohi.reset_index(inplace=True,drop=True)
#--------------------
#--- cartesian coords
#--------------------
swarm_lohi = GetCartesian( swarm_lohi )
# dd={'ROOT':407,
# 'exponent':4.0*2.7,
# 'dx':max(swarm_lohi.iloc[tree.pairs]['longitude'].max()-swarm_lohi.iloc[tree.pairs[0]]['longitude'],
# swarm_lohi.iloc[tree.pairs]['latitude'].max()-swarm_lohi.iloc[tree.pairs[0]]['latitude']),
# 'head_width':.15,'head_length':.3,
# 'shrinkA':0}
# dd={'ROOT':325,
# 'exponent':4.0*2.7,
# 'dx':max(swarm_lohi.iloc[tree.pairs]['longitude'].max()-swarm_lohi.iloc[tree.pairs[0]]['longitude'],
# swarm_lohi.iloc[tree.pairs]['latitude'].max()-swarm_lohi.iloc[tree.pairs[0]]['latitude']),
# 'head_width':.15,'head_length':.3,
# 'shrinkA':0}
#--- plot arrows
#for ii in xrange(1):
swarm_lohi = GetCartesian( swarm_lohi )
#dff = swarm_lohi.sort_values('magnitude',ascending=False)
#roott = [i[1] for i in sl]
#xxx=np.array(sl)
#sr=[[j,i] for i,j in zip(root,S)]
#sr.sort(reverse=True)
#sr[:10]
#for ROOT in root[cond]:
if 1: #for ii in sr[:20]:
# ROOT = ii[1]
# if not ROOT == 1:
# continue
# cls_id = xxx[xxx[:,1]==ROOT][0][2]
# tree.pairs = []
# stree[cls_id].plot(ax)
# tree.pairs = [ROOT]+tree.pairs
ROOT = 5 #1509 #5
dd={'ROOT':ROOT,
'exponent':4.0*0.8,
# 'dx':max(swarm_lohi.iloc[tree.pairs]['longitude'].max()-swarm_lohi.iloc[tree.pairs[0]]['longitude'],
# swarm_lohi.iloc[tree.pairs]['latitude'].max()-swarm_lohi.iloc[tree.pairs[0]]['latitude']),
'dx':0.2*max(swarm_lohi['x(km)'].max()-swarm_lohi['x(km)'].min(),
swarm_lohi['y(km)'].max()-swarm_lohi['y(km)'].min()),
'head_width':.15,'head_length':.3,
'shrinkA':0}
exponent=dd['exponent']
dx = dd['dx']
head_width = dd['head_width']
head_length=dd['head_length']
shrinkA=dd['shrinkA']
#for ii in xrange(1):
#ROOT = dd['ROOT']
#for item in dff.iloc[:30].itertuples(): #--- plot clusters associated with large events
item = swarm_lohi.loc[ROOT]
if 1:
# for item in dff.itertuples(): #--- plot clusters associated with large events
# if item.Index != ROOT:
# continue
(xc,yc)=(item['x(km)'],item['y(km)'])
# (xc,yc)=(swarm_lohi['longitude'].mean(),swarm_lohi['latitude'].mean())
tc = item['date'] #pd.to_datetime("2016-09-03 12:02:44.520")
dt = 1000 #--- setup
fig = plt.figure(figsize=(8,8)) #,frameon=False) #, dpi=300)
ax = fig.add_subplot(111)
#--- plot all events
ax.scatter(swarm_lohi['x(km)'], swarm_lohi['y(km)'], # 'x(km)'],swarm_lohi['y(km)'],
s=exponent**swarm_lohi['magnitude'],
alpha=0.1)
tt = tc #swarm_lohi['date'].loc[key_max]
xx={0:xc,1:yc}
junk,junk_t=PlotArrowsSpace( swarm_lohi, d_trig,
( tt+datetime.timedelta(days=-dt),tt+datetime.timedelta(days=+dt)),
(xx[0]-dx,xx[0]+dx),
(xx[1]-dx,xx[1]+dx) )
ax.set_xlim(xx[0]-dx,xx[0]+dx)
ax.set_ylim(xx[1]-dx,xx[1]+dx)
#--- set tick labels
xlist=np.linspace(xx[0]-dx,xx[0]+dx,4,endpoint=True)
ax.set_xticks(xlist)
xlist=[r'$%s$'%(int(i)) for i in xlist]
#
ylist=np.linspace(xx[1]-dx,xx[1]+dx,4,endpoint=True)
ax.set_yticks(ylist)
ylist=[r'$%s$'%(int(i)) for i in ylist]
# ax.set_yticklabels(ylist)
ax.tick_params(labelsize=24)
ax.tick_params(axis='y',labelright=True,labelleft=False,right=True,left=True)
ax.tick_params(axis='x',top=True)#,left=True)
ax.set_xticklabels(xlist,{'fontsize':20})
ax.set_yticklabels(ylist,{'fontsize':20})
#--- frame
# DrawFrame(ax, (0.16,0.16),(0.07,0.03),0.1)
DrawFrame(ax, (0.1,0.16),(0.09,0.03),0.1)
#fig.savefig('%s/spatialMap.png'%DIR_OUTPT_figs,bbox_inches='tight',dpi=150)
In [102]:
ROOT = 1505 #1
fig = plt.figure(figsize=(4,4))
ax = fig.add_subplot(111)
ax.set_xlim(100,1e6)
ax.set_ylim(1e-1,1e3)
ax.set_xscale('log')
ax.set_yscale('log')
for keys in stree:
tree_obj = stree[ keys ]
if tree_obj.data != ROOT:
continue
tree.rtm_dic = {} #--- initialize distance-time list
tree_obj.get_coords() #--- update
t_root = tree_obj.coord[ 0 ] #--- relative to the root
r_root = np.array(tree_obj.coord[ 1 ][:2] )
delta_t = []
delta_r = []
mmm=[]
for key in tree.rtm_dic:
t_afs = tree.rtm_dic[key][0]
r_afs = np.array(tree.rtm_dic[key][1][:2])
# if key == 5:
# print tree.rtm_dic[key][0]
# print tree.rtm_dic[key][1][:2]
# print tree.rtm_dic[key][2]
delta_t += [ ( t_afs - t_root ).total_seconds() ]
delta_r += [ ( ( ( r_afs - r_root ) ** 2 ).sum() ) ** 0.5 ]
mmm += [tree.rtm_dic[key][ 2 ]]
ax.scatter(delta_t,delta_r,s=3**np.array(mmm),alpha=0.1)
In [103]:
#print tree.rtm_dic
# swarm_lohi.sort_values(by='date',inplace=True)
# coord_length=swarm_lohi['longitude'].apply(lambda x:[x])+swarm_lohi['latitude'].apply(lambda x:[x])
# Magnitude = np.exp(swarm_lohi['magnitude'])/20000
KEYS=tree.rtm_dic.keys()
KEYS.sort()
coordd={}
Magnitudee={}
for i in KEYS:
coordd[i]=tree.rtm_dic[i][1][:2]
Magnitudee[i]=np.exp(tree.rtm_dic[i][2])/1000
makeDATA( open( '%s/map2.xyz'%DIR_OUTPT, 'w' ), None ).Map( coordd, 'ITIME=%s'%0, Magnitudee) #--- instantanuous
EVENT_ID = Magnitudee.keys()
EVENT_ID = map(int,EVENT_ID)
EVENT_ID.sort()
cords={}
mag={}
t0 = None
os.system('rm %s/temporalMap2.xyz'%DIR_OUTPT)
for j_event in EVENT_ID:
t = swarm_lohi['date'].iloc[ j_event ]
if not t0:
t0 = t
assert t >= t0, 't0=%s,t=%s'%( t0, t )
#--- temporal map
cords[ j_event ] = coordd[ j_event ]
mag[ j_event ] = Magnitudee[ j_event ]
itime=swarm_lohi[ 'date' ].iloc[ j_event ]
tstr='%s-%s'%(itime.strftime("%x"), itime.strftime("%X"))
makeDATA( open( '%s/temporalMap2.xyz'%DIR_OUTPT, 'a' ), None ).Map( cords, 'ITIME=%s'%itime, mag ) #--- instantanuous
t0 = t
In [104]:
swarm_loh = swarm_lohi.iloc[6:1510]
r0=np.array(swarm_lohi.iloc[5][['x(km)','y(km)']])
t0 = swarm_lohi.iloc[5][['date']]
m0 = swarm_lohi.iloc[5][['magnitude']]
dt=swarm_loh['date'].apply(lambda x:(x-t0))
dr=swarm_loh['x(km)'].apply(lambda x:x-r0[0])+swarm_loh['y(km)'].apply(lambda x:1j*(x-r0[1]))
dr=dr.abs()
dt_sec = dt['date'].apply(lambda x:x.total_seconds()/3600)
print m0
In [105]:
fig=plt.figure(figsize=(4,4))
ax=fig.add_subplot(111)
ax.set_xlim(1e-1,1e2)
ax.set_ylim(1e-1,1e2)
ax.set_xscale('log')
ax.set_yscale('log')
ax.scatter(dt_sec,dr,s=3.0**(swarm_loh['magnitude']),alpha=0.2)
Out[105]:
In [106]:
#--- r vs t (including indirect aftershocks)
dd = {}
for cls_id in stree:
index_m = np.array(m).searchsorted(stree[cls_id].coord[2]) - 1 #--- group clusters based on magnitude range
dd.setdefault(index_m,[]).append(cls_id)
colors = ['black','red','green','blue','cyan','brown']
for group_m, col in zip(dd, colors ): #--- loop over magnitude ranges
#--- plot
fig = plt.figure(figsize=(4,4))
ax = fig.add_subplot(111)
ax.set_xlim(1,1e5)
ax.set_ylim(1e-3,1e2)
ax.set_xscale('log')
ax.set_yscale('log')
cls_ids = dd[ group_m ] #--- cluster ids for a given range
delta_t = []
delta_r = []
for cls_id in cls_ids: #--- loop over each cluster
tree.rtm_dic = {} #--- initialize distance-time list
stree[cls_id].get_coords() #--- update
t_root = stree[cls_id].coord[ 0 ] #--- relative to the root
r_root = np.array( stree[cls_id].coord[ 1 ] )
for key in tree.rtm_dic:
t_afs = tree.rtm_dic[key][0]
r_afs = np.array(tree.rtm_dic[key][1])
delta_t += [ ( t_afs - t_root ).total_seconds() ]
delta_r += [ ( ( ( r_afs - r_root ) ** 2 ).sum() ) ** 0.5 ]
ax.scatter(delta_t,delta_r,color=col,alpha=0.05)
plt.show()
In [107]:
t0
Out[107]:
In [108]:
#--- r vs t (including indirect aftershocks)
dd = {}
for cls_id in stree:
index_m = np.array(m).searchsorted(stree[cls_id].coord[2]) - 1 #--- group clusters based on magnitude range
dd.setdefault(index_m,[]).append(cls_id)
colors = ['black','red','green','blue','cyan','brown']
for group_m, col in zip(dd, colors ): #--- loop over magnitude ranges
#--- plot
fig = plt.figure(figsize=(4,4))
ax = fig.add_subplot(111)
ax.set_xlim(1,1e5)
ax.set_ylim(1e-3,1e2)
ax.set_xscale('log')
ax.set_yscale('log')
cls_ids = dd[ group_m ] #--- cluster ids for a given range
delta_t = []
delta_r = []
for cls_id in cls_ids: #--- loop over each cluster
tree.rtm_dic = {} #--- initialize distance-time list
stree[cls_id].get_coords() #--- update
t_root = stree[cls_id].coord[ 0 ] #--- relative to the root
r_root = np.array( stree[cls_id].coord[ 1 ] )
for key in tree.rtm_dic:
t_afs = tree.rtm_dic[key][0]
r_afs = np.array(tree.rtm_dic[key][1])
delta_t += [ ( t_afs - t_root ).total_seconds() ]
delta_r += [ ( ( ( r_afs - r_root ) ** 2 ).sum() ) ** 0.5 ]
ax.scatter(delta_t,delta_r,color=col,alpha=0.05)
plt.show()
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